
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
(1) There are 3 different books on a shelf. If we keep their relative order unchanged and add 2 more different books, how many different arrangements are there?  
(2) There are 7 people of different heights standing in a row. The requirement is that the tallest person stands in the middle, and looking from the middle to both sides, each person is shorter than the one before. How many different arrangements are there?

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