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

(1) Find the maximum value of $f(x)$, and the set of values of $x$ when the function attains its maximum.

(2) In $\triangle ABC$, $a$, $b$, $c$ are the sides opposite to angles $A$, $B$, $C$ respectively, and $a=1$, $b=\sqrt{2}$, $f(A)=2$, find the measure of angle $C$.

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