
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

$$
K=\frac{\left(m^{2}+2 m-24\right) x^{2}-6(m+6) x+\left(m^{2}+10 m+24\right)}{\left(m^{2}-9 m+18\right) x^{2}-8(m-6) x+\left(m^{2}-3 m-18\right)}
$$

Determine all values of $m$ for which a) $K>0$ for any $x$; b) $K<0$ for any $x$.

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