
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 that in triangle $ \triangle ABC $, the sides opposite to angles $ A $, $ B $, and $ C $ are $ a $, $ b $, and $ c $ respectively, and that $\frac{a}{\cos A}=\frac{b}{2 \cos B}=\frac{c}{3 \cos C}$, calculate the measure of $ \angle A $.

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