
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 $f(x)\leqslant |f\left( \frac{\pi}{4} \right)|$ holds for any $x\in R$, and $f\left( \frac{\pi}{6} \right) > 0$, find the monotonically decreasing interval of $f(x)$.

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