
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 a positive integer  $n$ , let  $a_1,a_2,..,a_n$  be a sequence of nonnegative integers. A sequence of one or more consecutive terms of  $a_1,a_2,..,a_n$  is called  $dragon$  if their aritmetic mean is larger than 1. If a sequence is a  $dragon$ , then its first term is the  $head$  and the last term is the  $tail$ . Suppose  $a_1,a_2,..,a_n$  is the  $head$  or/and  $tail$  of some  $dragon$  sequence; determine the minimum value of  $a_1+a_2+\cdots +a_n$  in terms of  $n$ .

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