
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
It is known about the numbers \(a\) and \(b\) that the system of equations

\[
\left\{\begin{array}{l}
y^{2} = x^{2} + a x + b \\
x^{2} = y^{2} + a y + b
\end{array}\right.
\]

has no solutions. Find \(a\).

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