
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 $\tan{\alpha}$ and $\tan{\beta}$ are the roots of $x^2 - 3px + 4q = 0$, and $\tan{\alpha} \cdot \tan{\beta}$ is the value of $s$ in the equation $x^2 - 7rx + s = 0$ where $\cot{\alpha} + \cot{\beta} = r$, determine the value of $rs$.

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