
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 digits 0, 1, 2, 3, 4, 5:
(1) How many different natural numbers without repeated digits can be formed?
(2) How many different four-digit even numbers without repeated digits can be formed?
(3) How many different four-digit numbers without repeated digits that are greater than 4023 can be formed? (The final result is required)

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