
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) = A sin(ωx + φ) (x ∈ R) (where A > 0, $ω > 0, 0 < φ < \frac{π}{2}$) and the distance between two adjacent intersection points of the graph and the x-axis is $\frac{π}{2}$, and one of the highest points on the graph is ($\frac{π}{6}$, 3), find the analytical expression of the function f(x) = \_\_\_\_\_\_.

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