
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 angles $A$, $B$, $C$ and their respective opposite side lengths $a$, $b$, $c$. Also, it is given that $2\sin B\cos A=\sin A\cos C+\cos A\sin C$.

(I) Find the measure of angle $A$;

(II) If $a=6$, find the range of values for the perimeter of $\triangle ABC$.

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