Consider the following given function and given interval.

$f(t)=\frac{1}{t^2},[1,5]$

$($a$)$ Find the average value $f_{\text{a}\text{v}\text{e}}$ of $f$ on the given interval.

$($b$)$ Find $c$ in the given interval such that $f_{\text{a}\text{v}\text{e}}=f(c).($Enter your answers as a comma$-$separated list. Round your answers to three decimal places.$)$

$c=$