
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 $f(x)=\sqrt{3}\sin \omega x-\cos \omega x$ where $\omega\gt 0$, the distance between two adjacent symmetric axes of its graph is $\frac{\pi}{2}$.<br/>$(Ⅰ)$ If $f(x)=1$, find the value of $x$;<br/>$(Ⅱ)$ If the graph of $f(x)$ is shifted to the left by $m$ units $(m\gt 0)$ and coincides with the graph of the function $y=2\cos 2x$, find the minimum value of the real number $m$.

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