
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,  
(1) How many five-digit numbers can be formed?  
(2) How many five-digit numbers without repeated digits can be formed?  
(3) How many five-digit odd numbers without repeated digits can be formed?  
(4) Among the five-digit numbers without repeated digits, what is the position of 42130 when arranged in ascending order?  
(5) How many five-digit numbers without repeated digits can be formed, with odd digits in odd positions?

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