
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
Solve the system of equations
$$
\left\{\begin{array}{l}
x+y+z=a \\
x^{2}+y^{2}+z^{2}=b^{2} \\
x y=z^{2}
\end{array}\right.
$$

where \(a\) and \(b\) are known numbers. Also, determine the conditions on \(a\) and \(b\) such that \(x\), \(y\), and \(z\) are distinct positive numbers.

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