
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 $f(x)=\sqrt{3}\sin \omega x\cos \omega x-\cos ^{2}\omega x$ where $\omega\ \gt 0$, and the period is $\frac{π}{2}$.  
$(1)$ Find the analytical expression of $f(x)$ and write down the axis of symmetry of the function $f(x)$.  
$(2)$ If $|f(x)-m| \lt 2$ holds true when $\frac{π}{4}≤x≤\frac{{7π}}{{12}}$, find the range of values for $m$.

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