
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 inequality with respect to x: $kx^{2} - 2x + 6k < 0$ (where $k \neq 0$),  
(1) If the solution set of the inequality is $\{x | x < -3 \text{ or } x > -2\}$, find the value of $k$;  
(2) If the solution set of the inequality is $\{x | x \neq \frac{1}{k}\}$, find the value of $k$;  
(3) If the solution set of the inequality is the empty set, find the range of values for $k$.

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