
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 $f(x)=2\cos^2x-2\sin x\cos x+1$.
$(1)$ Let the equation $f(x)-1=0$ have two roots $x_{1}$, $x_{2}$ in the interval $(0,z)$. Find the value of $x_{1}+x_{2}$.
$(2)$ Translate the graph of the function $y=f(x)$ to the left by $m$ units ($m > 0$) so that the resulting function's graph is symmetric about the point $(0,2)$. Find the minimum value of $m$.

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