
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 $f(x)=\sin(2x+\phi)$, where $\phi$ is a real number and $|\phi| < \pi$, if $f(x) \leqslant |f(\frac{\pi}{6})|$ holds for all $x \in R$, and $f(\frac{\pi}{2}) > f(\pi)$, find:
1. The interval where $f(x)$ is monotonically increasing.
2. The zeros of $f(x)$.

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