
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Given the function
$$
f(x)=2 \cos x(\cos x+\sqrt{3} \sin x)-1 \quad (x \in \mathbf{R}).
$$
(1) Find the intervals where the function $f(x)$ is increasing.
(2) Points $P_{1}\left(x_{1}, y_{1}\right), P_{2}\left(x_{2}, y_{2}\right), \cdots, P_{n}\left(x_{n}, y_{n}\right), \cdots$ lie on the graph of the function $y=f(x)$ and satisfy
$$
x_{1}=\frac{\pi}{6}, \quad x_{n+1}-x_{n}=\frac{\pi}{2} \quad \left(n \in \mathbf{Z}_{+}\right).
$$
Find the value of $y_{1}+y_{2}+\cdots+y_{2018}$.


Present the answer in LaTex format: \boxed{Your answer}
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