
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
If $a$ and $b$ are two distinct zeros of the function $f(x) = x^2 - mx + n$ where $m > 0$ and $n > 0$, and $a$, $b$, $-1$ can be arranged to form an arithmetic progression or a geometric progression after proper sorting, find the solution set of the inequality $\frac{x-m}{x-n} \geq 0$.

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