
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 numbers $0, 1, 2, 3, 4, 5$:
$(1)$ How many different four-digit even numbers can be formed without repeating any digit?
$(2)$ How many six-digit numbers can be formed where odd digits are not adjacent to each other (without repeating any digit)?

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