
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 $f(x) = 2\sqrt{3}\sin x \cos x + 2\cos^2x - 1$,

(1) Find the maximum value of $f(x)$, as well as the set of values of $x$ for which $f(x)$ attains its maximum value;

(2) In $\triangle ABC$, if $a$, $b$, and $c$ are the lengths of sides opposite the angles $A$, $B$, and $C$ respectively, with $a=1$, $b=\sqrt{3}$, and $f(A) = 2$, determine the angle $C$.

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