
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
Research Question: Given the inequality about $x$, $ax^{2}-bx+c > 0$, whose solution set is $(1,2)$, let $y= \frac {1}{x}$, then $y∈( \frac {1}{2},1)$, hence the solution set of the inequality $cx^{2}-bx+a > 0$ is $( \frac {1}{2},1)$. By analogy with the above solution, given the inequality about $x$, $\frac {k}{x+a}+ \frac {x+b}{x+c} < 0$, whose solution set is $(-2,-1)∪(2,3)$, the solution set of the inequality about $x$, $\frac {kx}{ax-1}+ \frac {bx-1}{cx-1} < 0$ is \_\_\_\_\_\_.

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