
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 $ \triangle ABC $, with sides opposite to angles $ A $, $ B $, and $ C $ being $ a $, $ b $, and $ c $ respectively, it is given that $ (2b-c)\cos A = a\cos C $.

(I) Calculate the size of angle $ A $.

(II) If $ a = 3 $, find the maximum perimeter of $ \triangle ABC $.

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