
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
There are 3 boys and 4 girls standing in a line according to different requirements. How many different arrangements are there?  
(1) Person A and B must stand at the two ends;  
(2) Person A cannot stand at the left end, and person B cannot stand at the right end;  
(3) Person A and B must stand next to each other;  
(4) The 3 boys are arranged from left to right in descending order of height.

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