
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
Consider a paper punch that can be centered at any point
of the plane and that, when operated, removes from the
plane precisely those points whose distance from the
center is irrational. How many punches are needed to
remove every point?

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