
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 \(r\) be a complex number such that \(r^6 = 1\) and \(r \neq 1\). Compute
\[
(r - 1)(r^2 - 1)(r^3 - 1)(r^4 - 1)(r^5 - 1).
\]

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