
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 six numbers $1$ to $6$, select two even numbers and two odd numbers to form a four-digit number without repeating digits. The questions are:
1) How many different four-digit numbers can be formed?
2) Among these four-digit numbers, how many have two even numbers placed together?
3) How many four-digit numbers have two even numbers not adjacent to each other? (Express all results as numerical values)

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