
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 that the function $f(x)=A\sin (ωx+φ) (A > 0, ω > 0)$ has a minimum positive period of $2$, and the maximum value of $f(x)$ at $x= \frac{1}{3}$ is $2$.

1. Find the analytic expression of $f(x)$.
2. Does the function $f(x)$ have an axis of symmetry on the closed interval $[\frac{21}{4}, \frac{23}{4}]$? If so, find the axis of symmetry. If not, explain the reason.

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