(1) Find the intervals where the function $f(x)=2 \cos x(\cos x+\sqrt{3} \sin x)-1, x \in \mathbf{R}$ is monotonically increasing;
(2) Let points $P_{1}\left(x_{1}, y_{1}\right), P_{2}\left(x_{2}, y_{2}\right), \cdots, P_{n}\left(x_{n}, y_{n}\right), \cdots$ all lie on the graph of the function $y=f(x)$, and satisfy
$$
x_{1}=\frac{\pi}{6}, x_{n+1}-x_{n}=\frac{\pi}{2}\left(n \in \mathbf{N}^{*}\right)
$$

Find the value of $y_{1}+y_{2}+\cdots+y_{2018}$.
(1) $f(x)=\cos 2 x+\sqrt{3} \sin 2 x=2 \sin \left(2 x+\frac{\pi}{6}\right), f(x)$ is monotonically increasing in the interval $\left[-\frac{\pi}{3}+k \pi, \frac{\pi}{6}+k \pi\right], k \in \mathbf{Z}$;
(2) Let $t_{n}=2 x_{n}+\frac{\pi}{6}, t_{1}=2 x_{1}+\frac{\pi}{6}=\frac{\pi}{2}, t_{n+1}-t_{n}=\pi \Rightarrow t_{n}=\left(n-\frac{1}{2}\right) \pi$, so
$$
y_{n}=2 \sin \left(\frac{2 n-1}{2} \pi\right)=\left\{\begin{array}{ll}
2 & n=2 k-1 \\
-2 & n=2 k
\end{array} \quad(k \in \mathbf{Z})\right.
$$

Therefore, $y_{1}+y_{2}+\cdots+y_{2018}=0$.