
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, and 5, form six-digit numbers without repeating any digit.  
(1) How many such six-digit odd numbers are there?  
(2) How many such six-digit numbers are there where the digit 5 is not in the unit place?  
(3) How many such six-digit numbers are there where the digits 1 and 2 are not adjacent?

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