
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
Let $p, q$, and $r$ be the roots of the cubic polynomial $3x^3 + 4x^2 - 5x - 6$. Compute 
\[
(p+q+1)^3 + (q+r+1)^3 + (r+p+1)^3.
\]

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