
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
As is well known, a quadratic equation has no more than two roots. Can the equation \(\left\lfloor x^{2} \right\rfloor + p x + q = 0\) with \(p \neq 0\) have more than 100 roots? (\(\left\lfloor x^{2} \right\rfloor\) denotes the greatest integer less than or equal to \(x^{2}\)).

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