
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 $f(x)=\sin (ωx+φ)$ ($ω > 0$, $|φ| < \dfrac{\pi }{2}$) has a smallest positive period of $4\pi$, and for all $x\in R$, $f(x)\leqslant f(\dfrac{\pi }{3})$ holds true, find the coordinates of one symmetry center of $f(x)$.

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