
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 the cubic equation
\[
x^3 + Ax^2 + Bx + C = 0 \quad (A, B, C \in \mathbb{R})
\]
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}
user