
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
A hobby group has 3 instructors and 7 students taking a photo in two rows, with the 3 instructors standing in the front row and the 7 students standing in the back row.  
(1) If two students, A and B, want to stand at the two ends of the back row, how many different arrangements are there?  
(2) If students A and B cannot stand next to each other, how many different arrangements are there?  
(3) After all teachers and students have been arranged, the photographer decides the formation is not suitable and chooses to move 2 of the 7 people from the back row to the front row. If the relative order of the other people remains unchanged, how many different adjustment methods are there?  
(For each sub-question, please list the equations and give the numerical answer.)

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