
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
It is well-known that a quadratic equation has no more than 2 roots. Is it possible for the equation  $\lfloor x^2\rfloor+px+q=0$  with  $p\neq 0$  to have more than 100 roots?

*Alexey Tolpygo*

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