
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 $f(x)=2\sin\omega x\cos(\omega x+\frac{\pi}{3})$ where $(\omega>0)$ has a minimum positive period of $\pi$.  
$(1)$ Find the value of $\omega$;  
$(2)$ If the equation $f(x)=m$ has two distinct real roots in the interval $[0,\frac{\pi}{2}]$, find the range of values for $m$.

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