
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
Administrator A starts from vertex A and walks in the direction of AB, BC, and CA, making a round trip back to vertex A. Administrator B starts from point D on side BC and walks in the direction of DC, CA, AB, and BD, making a round trip back to the starting point D. Determine the total rotation of the bodies of administrators A and B during their journey.

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