
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
Let the function $f(x)=\cos x$, first keep the y-coordinate of $y=f(x)$ unchanged, change the x-coordinate to twice its original value, and then shift the graph to the right by $\dfrac{\pi }{3}$ units to get $y=g(x)$. Then, the center of symmetry of $y=g(x)$ is __________.

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