
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
Given the line \( y = k_{0}x + b \) intersects the hyperbola \( y = \frac{k^{2}}{x} \) at points \( M(m, -1) \) and \( N(n, 2) \). The solution set for the inequality
\[ x^{2} > k_{0}k^{2} + bx \]
is ______.

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