
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 a non-zero polynomial \( P(x) \). It is known that the identity \((x-2020) \cdot P(x+1)=(x+2021) \cdot P(x)\) holds for all \( x \). How many roots does the equation \( P(x)=0 \) have? Answer: 4042

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