
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 $f(x)=2\sin\frac{x}{2}\cos\frac{x}{2}+2\sqrt{3}\cos^{2}\frac{x}{2}-\sqrt{3}$, where $\triangle ABC$ has sides $a$, $b$, $c$ opposite angles $A$, $B$, $C$, respectively. It is known that $f(A)=\sqrt{3}$, and the circumradius of $\triangle ABC$ is $\sqrt{3}$.
$(1)$ Find the measure of angle $A$.
$(2)$ Find the maximum area of $\triangle ABC$.

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