
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) = 2cosx(cosx + $\sqrt{3}$sinx) - 1, where x belongs to the set of real numbers.

1. Find the maximum value of function f(x) and the set of x values where the maximum is achieved.
2. Suppose points Pn(xn, yn) (n = 1, 2, 3, ...) are all on the graph of the function y = f(x) and satisfy conditions x1 = $\frac{\pi}{6}$ and x(n+1) - xn = $\frac{\pi}{3}$ (n belongs to the set of natural numbers), find the value of y1 + y2 + ... + y2018.

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