Let $p$ be a prime number, and let $G$ be a finite group whose order is a power of $p$. Let $F$ be a field with characteristic $p$, and $V$ a nonzero vector space over $F$ equipped with linear action of $G$.( That is, we have an action $G\times V\to V$ of the group $G$ on the set $V$, written $(g,v)\mapsto g\cdot v$, such that for all $g\in G$, the map $v\mapsto g\cdot v$ is an $F$-linear transformation of the $F$-vector space $V$. )
Prove that there exists a nonzero subspace $W\subset V$ such that $G$ acts trivially on $W$.
I know the basics about group action but I don't know how to even start. Any help will be great for me. Thanks in advance.