
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
The necessary and sufficient condition for the graph of the function $y=f(x)$ to be symmetric with respect to the origin is that the function $y=f(x)$ is an odd function. This can be extended as follows: The necessary and sufficient condition for the graph of the function $y=f(x)$ to be symmetric with respect to the point $P(a,b)$ is that the function $y=f(x+a)-b$ is an odd function. Given that the graph of the function $f(x)=x^3-3x^2$, the center of symmetry is ________; and the value of $f(-2020)+f(-2019)+\cdots +f(2021)+f(2022)$ is ________.

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