
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 $\triangle ABC$, $AB=4$, $AC=6$.
(1) If $16\cos A=1$, find the length of $BC$ and the height $h$ on side $BC$;
(2) If $\triangle ABC$ is an acute triangle, find the range of the perimeter of $\triangle ABC$.

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