
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
Define \[Q(x) = (x - 1^2)(x - 2^2) \cdots (x - 50^2).\] How many integers \(n\) exist such that \(Q(n) \leq 0\)?
A) 1200
B) 1250
C) 1300
D) 1350
E) 1400

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