
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 \(a_{1}, a_{2}, a_{3}, a_{4}, b_{1}, b_{2}, b_{3}, b_{4}, c_{1}, c_{2}, c_{3}, c_{4}\) are all permutations of \(\{1, 2, 3, 4\}\), find the minimum value of \(\sum_{i=1}^{4} a_{i} b_{i} c_{i}\).

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