
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. They are lining up according to different requirements. Find the number of different ways they can line up.

$(1)$ All of them line up in a row, and person A and person B are not at the two ends;<br/>$(2)$ All of them line up in a row, boys stand together, and girls stand together;<br/>$(3)$ All of them line up in a row, and boys are not adjacent to each other.

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