
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
(1) How many natural numbers are there that are less than 5000 and have no repeated digits?
(2) From the digits 1 to 9, five digits are selected each time to form a 5-digit number without repeated digits.
   (i) If only odd digits can be placed in odd positions, how many such 5-digit numbers can be formed?
   (ii) If odd digits can only be placed in odd positions, how many such 5-digit numbers can be formed?

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