
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
Four boys and three girls sit in a row. Answer the following questions:  
(1) How many ways can the boys sit together?  
(2) How many arrangements are there where no two girls sit next to each other?  
(3) How many ways can the boys sit together and the girls sit together?  
(4) How many arrangements are there where boy A does not sit at the beginning and girl B does not sit at the end?

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