
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 constants $a$, $b$, $c$, and $d$, if the solution set of the inequality $$\frac {b}{x+a} + \frac {x+d}{x+c} < 0$$ is $(-1, -\frac {1}{3}) \cup (\frac {1}{2}, 1)$, then the solution set of the inequality $$\frac {bx}{ax-1} + \frac {dx-1}{cx-1} < 0$$ is \_\_\_\_\_\_.

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