
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
7 teachers and students stand in a row for a photo, including 1 teacher, 4 boys, and 2 girls. Under the following conditions, how many different standing arrangements are there? (Write out the necessary solution process)  
(1) The two girls must stand next to each other;  
(2) The 4 boys must not stand next to each other;  
(3) If the 4 boys are of different heights, they must stand in decreasing order of height from left to right;  
(4) The teacher does not stand in the middle, and the girls do not stand at the ends.

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