
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  $n$  be a natural number. The finite sequence  $\alpha$  of positive integer terms, there are  $n$  different numbers ( $\alpha$  can have repeated terms). Moreover, if from one from its terms any we subtract 1, we obtain a sequence which has, between its terms, at least  $n$  different positive numbers. What's the minimum value of the sum of all the terms of  $\alpha$ ?

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