
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
Given that \(a, b, c\) are integers such that \(abc = 60\), and that the complex number \(\omega \neq 1\) satisfies \(\omega^3 = 1\), find the minimum possible value of \(\left| a + b\omega + c\omega^2 \right|\).

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