
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
$f(x)=\sqrt{3}\sin2x-2\sin^{2}x+m,\_\_\_\_\_.$ Given that the sum of the maximum and minimum values of $f(x)$ is $0$ and $f(\frac{π}{2})=0$, choose one of the two conditions and answer the following:<br/>$(1)$ Find the value of $m$;<br/>$(2)$ Find the interval where the function $f(x)$ is monotonically increasing.<br/>$($Note: If you choose to answer conditions ① and ② separately, credit will be given for the first answer$)$.

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