
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
In $\triangle ABC$, let the sides opposite angles $A$, $B$, and $C$ be $a$, $b$, and $c$, respectively. It is given that $\frac{\cos C}{\sin C} = \frac{\cos A + \cos B}{\sin A + \sin B}$.
(1) Determine the size of $\angle C$;
(2) If $c=2$, find the maximum area of $\triangle ABC$.

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