
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 \( A = \{x \mid k x^2 - 2 x + 6 k < 0, k \neq 0\} \):
(1) If \( A \subseteq (2, 3) \), find the range of \( k \).
(2) If \( (2, 3) \subseteq A \), find the range of \( k \).
(3) If \( A \cap (2, 3) \neq \varnothing \), find the range of \( k \).

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