Allow me to explain Sage's wish to have a stronger mind in better detail.
Ancient Saiyans are born as mindless Ozaroo and while Sage wasn't born as an Ozaroo, the same concept still applies to him, then also adding being a legendary Saiyan would enhance the anger Sage would constantly feel even more, to the point where the immense amount of anger his brain was feeling would completely fry his brain, pretty much killing him.
Now the wish for giving him a stronger mind was to allow him to be able to be born with a mind strong enough to resist those emotions that he would constantly be feeling, but his mind isn't strong enough that it would be able to block the extra anger he feels when he transforms into an Ozaroo, or an LSSj for that matter.
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Sage-'FASTER!!, BODY GO FASTER!!!'
Using all the power I could muster, I fly through the explosion trying to save my daughter, even when the explosion injures me I ignore it and continue flying through. Reaching my hand forward, I'm only a couple of inches away from grabbing Mia, looking at her eyes I try my best to convey that everything will be fine, but right when my hand is only an inch away, the explosion suddenly stops before going in reverse.
Since I'm in the explosion radius, I get sucked forward, and right when everything returns to normal, I'm standing right where my daughter, Mia, should be, yet she isn't there, she's gone. Freaking out, I spread my ki senses to envelope the entire galaxy and then some, and I only reach my limit when my ki reaches the edge of the next galaxy, but I still don't sense any trace of Mia.
Sage-'NO,NO,NO,NO,NO!!! WHERE THE HELL IS SHE!!!'
Trunks-"MIA!!"
Goten-"MIA!!"
I hear someone yelling, but I'm too busy freaking out to be able to make sense of what they said. While I was trying my best to figure out what happened to my daughter, something terrible crept up in my mind, something I've been trying to not even take into account because just thinking of that possible ability, is dreadful enough.
Sage-'Dead. NO!!, she can't be, she's still alive, SHE HAS TO BE ALIVE!'
Even though I thought that I knew these were just false thoughts I was saying to myself to keep myself sane because I don't know what I would do if Mia was dead. But while I kept saying those empty words to myself, I could feel an absurd amount of anger seeping into my consciousness slowly and I was trying my best to hold it back, not wanting to lose myself in the destruction and slaughter that I knew would come. Even with trying my best, my mind was slowly getting filled with thoughts of destruction and slaughter, I was barely even conscious anymore when I heard something that caused me to finally snap.
Mira-"Towa has impressed me again, managing to create a bomb that completely wiped that little girl from existence, you wouldn't even be able to tell she was dead, everything about her is gone. I'm curious Sage, Towa told me that Saiyans get stronger the angrier they are, so how strong will you get when you know that your daughter died right before your eyes without you being able to do anything?"
The moment I heard those words from Mira, everything in my mind went blank, no thoughts, no emotion, nothing, until the anger that was seeping into me flooded my mind like a broken dam, I didn't even try to stop it anymore, in fact, I welcomed it. As my mind was getting overrun with anger, I could feel an absurd amount of strength come with it, and the last thing I remember was yelling my daughter's name before my consciousness faded completely, only anger fills my mind.
Sage-"MIAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA!!!!!!!!!!!!!!"
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Once my body finally healed up enough to actually move again, I got up from kneeled position with difficulty and started walking toward Goku and Vegeta who were in terrible condition. Using the pathetic amount of energy I have left, I start healing them till they can move as well.
Goku-"T-Thanks…Piccolo."
Vegeta-"Tsk,I…Don't…Need your…Help."
Ignoring them, I do my best to help them up, once they get up, we suddenly hear someone yelling 'DAD', looking to where the voices came from, we see Trunks, Goten, and Mia. They wanted to help us, but we told them to get away, but Mia ignored our warning and went to where Sage is. When she tried helping him, Mira attacked her, but even when completely outclassed in power, she still tried attacking him.
Piccolo-'She really takes after her father, but she needs to get out of here.'
When Sage got smacked away, Mira threw Mia in the distance and dropped a sphere right at her feet, and not even half a second later it exploded and not even 2 seconds later it stopped, but Mia was no longer present, instead Sage was standing where she once was.
Piccolo-"W-What…Happened…To her?"
Goku-"D-Do…You…Think…She-"
Vegeta-"D-Don't…Say that…Kakarot!"
Looking back to Sage, we overhear him talking to himself, and this continues for about a minute before Mira mocks Sage, but when that happens, Sage's ki slowly starts changing from his light red color to bright green, right when all of his Ki has changed he lets out a roar of his daughter's name.
Sage-"MIAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA!!!!!!!!!!!!!!"
After that, we suddenly sense an extraordinary amount of ki erupting from Sage, the amount of power we can sense is ridiculous, but even so, it keeps on growing. The amount of power he's releasing is distorting the very space, pathways to different dimensions are constantly getting ripped open constantly with ease. Before we even know it, the runes that were keeping the audience safe from harm's way, couldn't even last 5 seconds before it broke, and once it did the entire stadium got reduced to rubble, along with the audience being killed.
Everyone who was knocked out got flung away, and we were no different, after getting sent several hundreds of meters away, we finally managed to stop and stand our ground.
Piccolo-"W-Whats…Happening with…Sage!?"
Vegeta-"He's…Transforming…Into a…Super Saiyan!"
Goku-"I-It can't be…This is…Far more…Powerful than…A simple…Super Saiyan!"
Looking back at Sage, we can see his appearance constantly changing, his hair will grow, and shrink, and it would continue through that cycle, and his physique would expand and shrink back to normal constantly as well. This would continue for a little bit before he let out a roar filled with nothing but anger, and his ki rose once more before finally stopping at a stable level.
Once he finished transforming, his hair was different from a normal Ssj, it was green instead of yellow and far bigger, his physique increased in mass considerably, his muscles are at least twice as big as they usually are and he is even taller than me now, his eyes have no pupils in them anymore as well. But the most shocking thing about his transformation is the ki he is giving off, not only is it powerful, it gives off the feeling of a wild beast meant purely for destruction.
Piccolo-"Somethings…Wrong…With Sage."
Vegeta-"Tsk…We…Can tell."
As we continued watching Sage, we saw as he released another roar of his daughter's name, before indiscriminately releasing his ki within a 100-meter radius, destroying everything to rubble. Once he finished that, he looked at Mira and flew straight at him causing the space around him to collapse with his launch. When he got to Mira, he started attacking him, but even though he didn't seem to be conscious, his fighting skill didn't diminish one bit.
While they were fighting, we suddenly heard someone right next, luckily it was someone on our side.
Goku-"T-Trunks…What are…You doing here?"
F. Trunks-"Well I'll tell you later, but I came to stop Mira from intervening with the past of different timelines, but it seems like Sage has it handled, somewhat at least."
F. Trunks-"Here eat these Senzu beans, You guys are in terrible shape."
Eating the Senzu beans he threw at us, we stand up fully healed, and watch the battle between Sage and Mira.
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Note: Sage LSSj is that of DBZ Broly, so that means LSSj is an actual transformation, which means he could use Ikari on top of his LSSj, but of course only when he manages to transform into an LSSj without losing his reason.