
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 $a,$ $b,$ $c,$ $d$ be distinct integers, and let $\omega$ be a complex number such that $\omega^4 = 1$ and $\omega \neq 1.$ Find the smallest possible value of
\[|a + b \omega + c \omega^2 + d \omega^3|.\]

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