
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) Form a seven-digit number with no repeated digits using the numbers 1, 2, 3, 4, 5, 6, 7. Calculate the number of such seven-digit numbers where the three even numbers are adjacent, and the number of such seven-digit numbers where the three even numbers are not adjacent to each other;  
(2) Given six different books divided into three groups, how many different distribution methods are there under the following conditions?  
① Two books per group;  
② One group with one book, one group with two books, and one group with three books.

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