
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
Given that \(a\) is an integer, if there exist two distinct integers \(x\) and \(y\) satisfying the system of equations \(\left\{\begin{array}{l}x - y^2 = a, \\ y - x^2 = a,\end{array}\right.\) and \(|x| \leq 10\), what is the minimum value of \(a\)?

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