
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 about $x$, $kx^2-2x+6k<0$, where $k>0$,  
(1) If the solution set of the inequality is $\{x|2<x<3\}$, find the value of the real number $k$;  
(2) If the inequality holds for all $2<x<3$, find the range of values for the real number $k$;  
(3) If the solution set of the inequality is a subset of the set $\{x|2<x<3\}$, find the range of values for the real number $k$.

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