
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
For the inequality in terms of $x$, $kx^{2}-2x+6k < 0$;  
$(1)$ If the solution set of the inequality is $(2,3)$, find the value of the real number $k$;  
$(2)$ If $k > 0$ and the inequality holds for all $2 < x < 3$, find the range of values for the real number $k$.

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