
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
Let  $a_{1}$ ,  $a_{2}$ , …,  $a_{6}$ ;  $b_{1}$ ,  $b_{2}$ , …,  $b_{6}$  and  $c_{1}$ ,  $c_{2}$ , …,  $c_{6}$  are all permutations of  $1$ ,  $2$ , …,  $6$ , respectively. Find the minimum value of  $\sum_{i=1}^{6}a_{i}b_{i}c_{i}$ .

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