
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 that the three interior angles $A$, $B$, $C$ of $\triangle ABC$ form an arithmetic sequence, and the side $b$ opposite to angle $B$ equals $\sqrt{3}$, and the function $f(x)=2 \sqrt{3}\sin ^{2}x+2\sin x\cos x- \sqrt{3}$ reaches its maximum value at $x=A$, then the area of $\triangle ABC$ is __________.

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