
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
The maximum value of the function $f(x)=A\sin (\omega x+ \frac {\pi}{6})$ ($A > 0,\omega > 0$) is $2$, and its smallest positive period is $2\pi$.  
(I) Find the analytical expression of the function $f(x)$;  
(II) If $g(x)=\cos x\cdot f(x)$, find the maximum and minimum values of $g(x)$ in the interval $\left[- \frac {\pi}{6}, \frac {\pi}{4}\right]$.

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