
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 \( a, b, c > 0 \). If
\[ 57a + 88b + 125c \geqslant 1148, \]

find the minimum value of \( a^3 + b^3 + c^3 + 5a^2 + 5b^2 + 5c^2 \).

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