
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 the equation as a quadratic in terms of \(a\). Then its discriminant is \(x^{2} (25 - 24x^{2})\). Since \(x\) is an integer, this discriminant is nonnegative only when \(x = 0\) or \(x = \pm 1\).

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