
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 $$f(x)=4\cos\omega x\cos(\omega x+ \frac {\pi}{3}), (\omega>0)$$ has the smallest positive period of $\pi$.  
(1) Find the value of $\omega$;  
(2) Discuss the monotonicity of $f(x)$ in the interval $$[0, \frac {5\pi}{6}]$$.

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