
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 positive integer. We call  $(a_1,a_2,\cdots,a_n)$  a *good*  $n-$ tuple if  $\sum_{i=1}^{n}{a_i}=2n$  and there doesn't exist a set of  $a_i$ s such that the sum of them is equal to  $n$ . Find all *good*  $n-$ tuple.
(For instance,  $(1,1,4)$  is a *good*  $3-$ tuple, but  $(1,2,1,2,4)$  is not a *good*  $5-$ tuple.)

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