
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 $f(x)=\sin (2x+φ)$, where $φ$ is a real number. If $f(x)\leqslant \left| f\left( \frac{π}{6} \right) \right|$ holds for all $x\in R$, and $f\left( \frac{π}{2} \right) > f(π)$, determine the interval where $f(x)$ is monotonically increasing.

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