
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: \[ x+y+z=a  \] \[ x^2+y^2+z^2=b^2  \] \[ xy=z^2  \] where  $a$  and  $b$  are constants. Give the conditions that  $a$  and  $b$  must satisfy so that  $x,y,z$  are distinct positive numbers.

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