
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 7 students of different heights standing in a row from left to right according to the following requirements. Calculate the number of ways they can stand under each condition. (Please write out the necessary solution process, and represent the final result numerically)
(1) Student A cannot stand at either end;
(2) Student A cannot stand on the left end, and Student B cannot stand on the right end;
(3) Students A and B must stand next to each other, and Students C and D must not stand next to each other;
(4) From the center to both sides, they must stand in order from tallest to shortest.

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