
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 vector $\overrightarrow {a}$=（sinωx+cosωx，sinωx）, vector $\overrightarrow {b}$=（sinωx-cosωx，2$\sqrt {3}$cosωx）, and function f(x) = $\overrightarrow {a}$•$\overrightarrow {b}$+1 (x∈R) whose graph is symmetric about the line x=$\frac {π}{3}$, where constant ω∈(0,2).
(1) Find the range of f(x) when x∈[0,$\frac {π}{2}$];
(2) Under the condition of (2), find the equation of the symmetry axis and the monotonic intervals of function f(x).

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