
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 3 boys and 4 girls in a row. Calculate the number of different arrangements under the following conditions:
(1) Person A and Person B must stand at the two ends;  
(2) All boys must stand together;  
(3) No two boys stand next to each other;  
(4) Exactly one person stands between Person A and Person B.

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