
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

The following equations apply to the real numbers \(x, y, a\):

\[
\begin{aligned}
x + y &= a \\
x^{3} + y^{3} &= a \\
x^{5} + y^{5} &= a
\end{aligned}
\]

Determine all possible values of \(a\).

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