
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
The amplitude of the function $y=A\sin(\omega x+\varphi)$, where $A>0$ and $\omega>0$, is $3$. The minimum positive period is $\frac{2\pi}{7}$, and the initial phase is $\frac{\pi}{6}$. Find the analytical expression of the function.

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