Show that $E\left[\left\vert\sum y_kx_k\right\vert^4\right]\le3E\left[\left\vert\sum y_kx_k\right\vert^2\right]^2$ for $(x_k)$ i.i.d. random signs

Question

$x_1, x_2, x_3, x_4,\,\ldots\,,x_m$ are either positive or minus signs and they are random and independent; $y_1, y_2, y_3, y_4, \ldots,y_m \in \mathbb{R}$.

Prove the following:

$$E\left[ \Bigl|\sum_{k=1}^m y_k\, x_k\Bigr|^4 \right] \leq 3 E \left[ \Bigl| \sum_{k=1}^m y_k\, x_k \Bigr |^2 \right]^2 $$

Is there any sort of expected value basic properties i can use here to prove this? The above equation IMO looks like $E\left[ E[y_k] \right]$ so am I proving that $E\left[ {E[y_k]}^4 \right] \leq 3E\left[ {E[ y_k ]}^2 \right]^2$?