
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]


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Given $$\overrightarrow {a}=(2\sin\omega x,\cos\omega x+\sin\omega x)$$, $$\overrightarrow {b}=(\cos\omega x,\cos\omega x-\sin\omega x)$$, (ω＞0),  
the function $$f(x)= \overrightarrow {a}\cdot \overrightarrow {b}$$, and the smallest positive period of function $f(x)$ is $\pi$.  
(I) Find the analytical expression of function $f(x)$.  
(II) Determine the monotonic intervals of function $f(x)$ on $$[0, \frac {\pi }{2}]$$.

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