
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
In an acute triangle $\triangle ABC$, the sides opposite to angles A, B, and C are denoted as $a$, $b$, and $c$ respectively. It is given that $\overrightarrow{m} = (\sqrt{3}a, c)$ and $\overrightarrow{n} = (\sin A, \cos C)$, with $\overrightarrow{m} = 3 \overrightarrow{n}$.
(1) Find the angle $C$;
(2) Determine the range of the perimeter of triangle $\triangle ABC$.

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