
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 \( a, b, c \in \mathbf{R} \), and the existence of \( \alpha, \beta, \gamma \in \{-1,1\} \) such that \( a \alpha + b \beta + c \gamma = 0 \), find the minimum value of \( f = \left(\frac{a^3 + b^3 + c^3}{abc}\right)^2 \).

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