
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 that the solution set of the inequality $ax^{2}+bx+c\leqslant 0$ with respect to $x$ is $\{x\left|\right.x\leqslant -1$ or $x\geqslant 3\}$, then the solution set of $cx^{2}-bx+a \lt 0$ is ______.

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