
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 a cubic polynomial equation
$$
x^{3}+A x^{2}+B x+C=0 \quad (A, B, C \in \mathbf{R})
$$
with roots \(\alpha, \beta, \gamma\), find the minimum value of \(\frac{1+|A|+|B|+|C|}{|\alpha|+|\beta|+|\gamma|}\).

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