
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
We know that the graph of the function $y=f(x)$ is symmetric with respect to the origin if and only if the function $y=f(x)$ is an odd function. Some students have found that this can be extended to: the graph of the function $y=f(x)$ is symmetric with respect to the point $P(a,b)$ if and only if the function $y=f(x+a)-b$ is an odd function. The symmetric center of the graph of the function $f(x)=x^{3}-6x^{2}$ is ______.

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