
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
Consider the equation
\[
(x - \sqrt[3]{17})(x - \sqrt[3]{67})(x - \sqrt[3]{137}) = 1
\]
It has three distinct solutions $p,$ $q,$ and $r.$ Calculate the value of $p^3 + q^3 + r^3.$

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