
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 $y=A\sin (\omega x+ \phi )+B (A > 0,\omega > 0,|\phi| < \dfrac{\pi }{2})$ with a maximum value of $3$, a minimum value of $1$, and a smallest positive period of $\dfrac{\pi }{2}$. The line $x=\dfrac{\pi }{3}$ is one of its symmetric axes. Find the analytical expression of the function.

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