Find all harmonic functions $u$ on $\mathbb{C}$ satisfying $u(z) \le x$

Question

I'm new to complex analysis so I might be overlooking something. I'm thinking I could somehow use Liouville to make $u$ constant by taking $e^f$ where $f=u+iv$, with $v$ being the harmonic conjugate of $u$, but I seem to be stuck here. Another thing I tried was to use the Identity Theorem since taking $u(z)$ over purely imaginary numbers give a constant bound, but it says nothing about the actual sequence $u(iy)$. Any help?