
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
If $a$, $b$, $c \in \mathbb{R}$, and the solution set of the inequality $ax^{2}+bx+c \gt 0$ with respect to $x$ is $\left(-2,1\right)$, then the solution set of the inequality $ax^{2}+\left(a+2b\right)x-c \lt 0$ with respect to $x$ is ______.

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