
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 digits 1 to 9, take three even numbers and four odd numbers, and answer the following:
1. How many 7-digit numbers without any repeating digits can be formed?
2. Among such 7-digit numbers mentioned above, how many of them have the three even numbers together?
3. Among the 7-digit numbers from question 1, how many have all even numbers together and all odd numbers together?
4. Among the 7-digit numbers from question 1, how many have no two even numbers adjacent?

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