
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 $f(x)=\sin (wx+ϕ)$, where $w > 0$, $|ϕ| < \dfrac{π}{2}$, the smallest positive period is $4π$, and for all $x$ in the set of real numbers, $f(x)\leqslant f\left(\frac{π}{3}\right)$ holds true, find the coordinates of one of the symmetry centers of $f(x)$.

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