
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 acute triangle ABC, the sides opposite to angles A, B, C are a, b, c respectively. Given that $\overrightarrow {m}=( \sqrt {3}a, c)$, $\overrightarrow {n}=(sinA, cosC)$, and $\overrightarrow {m}=3 \overrightarrow {n}$. Find (1) C, and (2) the range of the perimeter of triangle ABC.

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