
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 solution set for the inequality in terms of $x$, $ax^{2}+bx+c > 0$, is $(-1,2)$. Solve the inequality in terms of $x$, $ax^{2}-bx+c > 0$.

A solution method is as follows: From the given solution set for $ax^{2}+bx+c > 0$ being $(-1,2)$, it follows that the solution set for $a(-x)^{2}+b(-x)+c > 0$ is $(-2,1)$, which means the solution set for $ax^{2}-bx+c > 0$ is $(-2,1)$.

Referencing the above solution, if the solution set for the inequality in terms of $x$, $\frac {k}{x+a}+ \frac {x+b}{x+c} < 0$, is $(-3,-1)∪(1,2)$, then find the solution set for the inequality in terms of $x$, $\frac {kx}{ax+1}+ \frac {bx+1}{cx+1} < 0$.

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