
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
Find all integer values of the parameter \(a\) for which the system
\[
\begin{cases}
x - 2y = y^2 + 2, \\
ax - 2y = y^2 + x^2 + 0.25a^2
\end{cases}
\]
has at least one solution. In the answer, indicate the sum of the found values of the parameter \(a\).

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