
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 with different heights. How many different arrangements can be made under the following conditions?  
(1) The 7 students stand in a row, with the tallest in the middle, and their heights decrease towards both ends;  
(2) Select any 6 students and arrange them into two rows and three columns, ensuring that the student in the front row is shorter than the student in the back row for each column.

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