
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
From the nine digits 1 to 9, take three even numbers and four odd numbers. Determine:
(1) How many distinct seven-digit numbers can be formed?
(2) Among these seven-digit numbers, how many have the three even numbers grouped together?
(3) From the seven-digit numbers in (1), how many have no two even numbers adjacent to each other?

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