
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 $ax^{2}-bx-1 > 0$ is $\left\{ x\left|\left. -\frac{1}{2} < x < -\frac{1}{3} \right.\right.\right.\right\}$, determine the solution set of the inequality $x^{2}-bx-a\geqslant 0$.

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