
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
Roll a die three times in a row, and arrange the numbers obtained in sequence to form a three-digit number. In this case:

(1) How many different three-digit numbers can be formed where all digits are distinct?

(2) How many different numbers can be formed in total?

(3) How many three-digit numbers can be formed where exactly two digits are the same?

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