
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
Let us solve the following system of equations:

\[
\begin{aligned}
x + y + z &= a \\
x^2 + y^2 + z^2 &= b^2 \\
xy &= z^2 
\end{aligned}
\]

where \(a\) and \(b\) are given numbers. What condition must the numbers \(a\) and \(b\) satisfy for the solution \(x, y, z\) of the system to be positive and distinct?

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