ok, so i just decided to try some new strings. i have a standard fat strat (HSS) with a normal fender trem. i have always played D'addario 0.09 strings (i learned acoustic before electric) and decided to try some larger strings from another brand. everyone's always talking about ernie ball slinkys, so i got some power slinkys (0.11) and strung up my guitar with them. i had always heard that larger strings gave a better tone, but wow! i always thought "i should learn to play a lot better before i start worrying about things like my strings" and i guess, even though i had gotten a lot better, i still thought that because i had been thinking it so long. i was really wrong, they sound so much better, the only problem is now my guitar has gotten all messed up. it's definitely not set up for these size strings. the trem is all the way out, giving me absolute crap intonation. i figure i should get a couple extra springs and plop them in the trem cavity and it'll fix itself, but then i started thinking that the 2 extra springs probably wouldn't get it exactly right. now as for action, i'm not picky, i play lots of styles so a medium range action is good for me, but will i need to reset the intonation after adding the springs? will 2 springs be enough? is there anything else i'll need to do? the nut seems to fit the strings (standard nut came on the guitar from the factory in Mexico) but i wouldn't know if anything was wrong unless the strings were popping out. do i need to do anything to the nut? will i need to mess with the spring tension in the trem cavity?

EDIT: holy jesus, sorry for the long post!
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you just need to tighten the screws in the back, add 1 or 2 springs, adjust the action then intonation.

example of 5 springs, 2 screws.

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You shouldnt have to do anything to the nut.

Loosen the strings and unscrew the claw a little bit, that's the part that holds the springs. Put the new springs in, tighten the strings then screw in the claw until the bridge is where it's supposed to be.