
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 ABC with all angles unequal, the sides opposite to angles A, B, C are a, b, c respectively. Given that b = 2a*cos(A).
(I) Find the range of angle A.
(II) Find the range of the function $f(A) = 2\cos(A)(\sqrt{3}\cos(A) + \sin(A))$.

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