
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 $3x^3 - 5x^2 + 50x - 7$. Compute \[(p+q-2)^3 + (q+r-2)^3 + (r+p-2)^3.\]

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