
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
Arrange five teachers A, B, C, D, and E in a row with 25 same seats. After that, 25 students will sit in the seats for a photograph with the teachers. Requirement: A, B, C, D, and E must appear in alphabetical order from left to right in the row, and there must be at least two seats between each pair of adjacent teachers. How many different arrangements are possible? (Note: The arrangement here refers only to the placement of the teachers among the empty seats, not considering the subsequent students).

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