
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 $\triangle ABC$, the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively, and the area of $\triangle ABC$ is $S_{\triangle ABC}$. Given that:
1. $\sqrt{3}\overrightarrow{CA}⋅\overrightarrow{CB}=2{S}_{\triangle ABC}$,
2. $\left(\sin C+\sin A\right)\left(\sin C-\sin A\right)=\sin B\left(\sin B-\sin A\right)$,
3. $\left(2a-b\right)\cos C=c\cos B$.

Choose any one of the three conditions and answer the following questions:
1. Find angle $C$.
2. If $c=2$, find the maximum value of the area of $\triangle ABC$.

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