
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 relation to \( a \). Then its discriminant equals \( x^{2} \left(49 - 40 x^{2} \right) \). Since \( x \) is an integer, this discriminant is non-negative only when \( x = 0 \) or \( x = \pm 1 \).

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