
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
Construct positive integers with no repeated digits using the six numbers 0, 1, 2, 3, 4, 5.  
(1) How many four-digit numbers can be formed? How many of them are even numbers?  
(2) How many four-digit numbers are larger than 4301?  
(3) Calculate the sum of all these four-digit numbers.  
Note: Answer using numerals only.

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