
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
Find distinct positive integers  $n_1<n_2<\dots<n_7$  with the least possible sum, such that their product  $n_1 \times n_2 \times \dots \times n_7$  is divisible by  $2016$ .

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