
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 integers such that $p \neq q \neq r \neq p$ and at least one of them is zero. Let $\omega$ be a complex number such that $\omega^3 = 1$ and $\omega \neq 1.$ Find the smallest possible value of
\[|p + q \omega^2 + r \omega|.\]

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