
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 $f(x)=2\sin (wx+\phi )+1,(w > 0,|\phi |\leqslant \frac{\pi }{2})$, the distance between two adjacent intersections of its graph with the line $y=3$ is $\pi$. If $f(x) > 2$ holds for $\forall x\in\left( \frac{\pi}{24}, \frac{\pi}{3}\right)$, determine the range of $\phi$.

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