
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
Using the five digits $0$, $1$, $2$, $3$, $4$ to form a five-digit number without repeating digits.<br/>$(1)$ How many even numbers are there in the five-digit number formed?<br/>$(2)$ How many numbers greater than $31000$ are there in the five-digit number formed?<br/>$(3)$ How many numbers are there in the five-digit number formed where the digits $2$ and $4$ are not adjacent?

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