<s>[INST] In a given triangle $ABC$, the median to side $BC$ is $AM$, the median to side $AC$ is $BN$, and the median to side $AB$ is $CP$. If the following equations are satisfied: $AM^2 + BN^2 = 2(AN^2 + CM^2)$ and $AB = 2$, what is the length of $AC$?[/INST]