
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 \( f(x) = 2 \cos x(\cos x + \sqrt{3} \sin x) - 1, x \in \mathbf{R} \):
1. Find the intervals where the function \( f(x) \) is monotonically increasing.
2. Suppose the points \( P_{1}(x_{1}, y_{1}), P_{2}(x_{2}, y_{2}), \cdots, P_{n}(x_{n}, y_{n}), \cdots \) lie on the graph of the function \( y = f(x) \) and satisfy
   \[
   x_{1} = \frac{\pi}{6}, \quad x_{n+1} - x_{n} = \frac{\pi}{2} \quad (n \in \mathbf{N}^{*})
   \]
   Find the value of \( y_{1} + y_{2} + \cdots + y_{2018} \).

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