
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 $f(x)=2\sin (\omega x+\varphi)+1$ ($\omega > 0$, $|\varphi| \leqslant \frac {\pi}{2}$), the distance between two adjacent intersection points of its graph and the line $y=3$ is $\pi$. If $f(x) > 2$ for $\forall x\in\left( \frac {\pi}{24}, \frac {\pi}{3}\right)$ always holds, find the range of $\varphi$.

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