
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 $f(x)$ satisfy $f(2-x)=f(2+x)$ and $f(5-x)=f(5+x)$ for all $x\in (-\infty, +\infty)$. Moreover, it is given that $f(1)=f(3)=0$ on the closed interval $[0,5]$. Determine the number of roots of the equation $f(x)=0$ on the closed interval $[-2020,2020]$.

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