
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 $f(x)=2\cos^2 ωx+\sqrt{3}\sin2ωx-1$ ($ω>0$) with a minimum positive period of $\frac{π}{2}$, if the graph of function $f(x)$ is shifted to the right by $\frac{π}{12}$ units to obtain the graph of function $g(x)$, determine the point on the graph of function $g(x)$ closest to the origin, which is the symmetric center.

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