
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
The corners of a fixed convex (but not necessarily regular)  $n$ -gon are labeled with distinct letters. If an observer stands at a point in the plane of the polygon, but outside the polygon, they see the letters in some order from left to right, and they spell a "word" (that is, a string of letters; it doesn't need to be a word in any language). For example, in the diagram below (where  $n=4$ ), an observer at point  $X$  would read " $BAMO$ ," while an observer at point  $Y$  would read " $MOAB$ ."

[center]Diagram to be added soon[/center]

Determine, as a formula in terms of  $n$ , the maximum number of distinct  $n$ -letter words which may be read in this manner from a single  $n$ -gon. Do not count words in which some letter is missing because it is directly behind another letter from the viewer's position.

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