
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 $\triangle ABC$ is an acute-angled triangle with sides $a$, $b$, and $c$ opposite angles $A$, $B$, and $C$ respectively, and with $c = 2$, the expression $a \cos B + b \cos A = \frac{\sqrt{3}c}{2\sin C}$ holds. Determine the range of the perimeter of $\triangle ABC$.

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