
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 vectors $\overrightarrow {a}$=($\sqrt {3}$sinx, $\sqrt {3}$cos(x+$\frac {\pi}{2}$)+1) and $\overrightarrow {b}$=(cosx, $\sqrt {3}$cos(x+$\frac {\pi}{2}$)-1), define f(x) = $\overrightarrow {a}$$\cdot \overrightarrow {b}$.
(1) Find the minimum positive period and the monotonically increasing interval of f(x);
(2) In △ABC, a, b, and c are the sides opposite to A, B, and C respectively, with a=$2\sqrt {2}$, b=$\sqrt {2}$, and f(C)=2. Find c.

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