
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 $f(x)=A\sin (\omega x+\varphi)$ $(A > 0,\omega > 0,|\varphi| < \pi)$, within the same period, when $x= \frac {\pi}{12}$, $f(x)$ reaches its maximum value $3$; when $x= \frac {7\pi}{12}$, $f(x)$ reaches its minimum value $-3$.  
(I) Find the analytical expression of the function $f(x)$;  
(II) If $x\in[- \frac {\pi}{3}, \frac {\pi}{6}]$ and the function $h(x)=2f(x)+1-m$ has two zeros, find the range of the real number $m$.

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