
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
From the numbers $0-9$, select $3$ numbers. Find:<br/>$(1)$ How many ways are there to arrange the $3$ numbers without repetition?<br/>$(2)$ How many three-digit numbers without repetition can be formed?<br/>$(3)$ How many three-digit odd numbers without repetition can be formed?<br/>($Note: Provide appropriate explanations in words, and express the final results in numbers)

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