
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
As shown in the diagram, the vertices of a hexagon are labeled $A, B, C, D, E, F$. Initially, the six Chinese characters of "华罗庚金杯赛" are placed at the vertices $A, B, C, D, E, F$ respectively. If each character is then moved to an adjacent vertex from its original position, how many different placement arrangements are there where each vertex ends up with one character, with each character being adjacent to its original position?

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