
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 the planar vectors $\overrightarrow {a}$=(sinx, 2$\sqrt {3}$cosx) and $\overrightarrow {b}$=(2sinx, sinx), and the function f(x) = $\overrightarrow {a}$•$\overrightarrow {b}$+1.
(1) Find the monotonic intervals of f(x);
(2) In acute triangle ABC, a, b, and c are the sides opposite angles A, B, and C, respectively. If f(A)=4 and a=2, find the range of the perimeter of triangle ABC.

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