
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
How many points on the parabola \( y = x^2 \) (other than the origin) have the property that the tangent at these points intersects both coordinate axes at points with integer coordinates whose absolute values do not exceed 2020?

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