
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 $$f(x)= \overrightarrow {a}\cdot \overrightarrow {b}$$, where vectors $$\overrightarrow {a}=( \sqrt {3}\sin2x, 1)$$, $$\overrightarrow {b}=(1, \cos2x)$$ ($x\in\mathbb{R}$),
(1) Find the intervals of monotonic increase for the function $y=f(x)$;
(2) In triangle ABC, the sides opposite angles A, B, and C are denoted as a, b, and c, respectively. Given $f(A)=2$, $a= \sqrt {7}$, $b= \sqrt {3}$, find the value of side length c.

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