
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 point $A(\frac{π}{{24}},0)$ lies on the graph of the function $f\left(x\right)=\sin \left(\omega x+\varphi \right)$ where $\omega\ \ \gt 0$ and $0 \lt \varphi\ \ \lt \pi$. The line $x=\frac{π}{6}$ is a symmetry axis of the graph of the function $f\left(x\right)$, and $f\left(x\right)$ is monotonically increasing on the interval $({\frac{π}{6},\frac{π}{3}})$. Find $f\left(x\right)$.

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