
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 $f(x)=A\sin (ωx+φ) (A > 0, ω > 0, 0 \leqslant φ \leqslant \frac {π}{2})$, points $P(x\_1,4)$ and $Q(x\_2,4)$ are two adjacent highest points on the graph of $f(x)$, and $|x\_1-x\_2|=π$. Additionally, $x=\frac {π}{3}$ is a zero of the function $f(x)$. Determine the smallest positive value $x\_0$ at which the function $f(x)$ attains its maximum value.

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