
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 $\left\{a_{i}\right\}$, $\left\{b_{i}\right\}$, and $\left\{c_{i}\right\}$ (for $i=1,2, \cdots, 10$) are all permutations of the set $\{1,2, \cdots, 10\}$, find the minimum value of $\sum_{i=1}^{10} a_{i} b_{i} c_{i}$.

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