
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 function $$f(x)=4\cos\omega x\sin(\omega x- \frac {\pi}{6})(\omega＞0)$$ has the smallest positive period of $\pi$.  
(1) Find the interval of monotonic increase for the function $f(x)$ in the interval $x\in(0,\pi)$.  
(2) Find the maximum and minimum values of $f(x)$ on the interval $$\left[ \frac {\pi}{8}, \frac {3\pi}{8}\right]$$.

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