
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 every real values that  $a$  can assume such that  $$ \begin{cases}
x^3 + y^2 + z^2 = a
x^2 + y^3 + z^2 = a
x^2 + y^2 + z^3 = a
\end{cases} $$  has a solution with  $x, y, z$  distinct real numbers.

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