
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
We will define a "snake" in a convex $n$-gon as a non-closed, non-self-intersecting polygonal chain consisting of $n-1$ segments, where the set of vertices coincides with the set of all vertices of the $n$-gon. Find the number of distinct snakes in an $n$-gon. (Snakes are considered equal if they coincide as geometric loci. For example, the number of snakes in a triangle is 3.)

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