
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
12 chairs are numbered from 1 to 12. A grasshopper can jump from chair $k$ to chair $n$ if $k-n$ is one of the four numbers $-8, -5, 5, 8$. It is known that it has visited each chair exactly once. What are the possible initial positions?

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