
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 a triangle $\triangle ABC$ with sides $a, b, c$ opposite to angles $A, B, C$ respectively, it satisfies $2\cos C \cdot (a \cos B + b \cos A) = c$.
① Find angle $C$;
② If $c = \sqrt {7}$ and $ab = 6$, find the perimeter of $\triangle ABC$.

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