
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
We know that the most common dice today is a six-sided die, which is a regular cube with one to six dots (or numbers) on its faces, such that the sum of the numbers on opposite faces equals seven. Obviously, rolling a six-sided die can only produce one of six numbers (on the top face). We now ask you to design a "decimal die" that, when rolled, can produce one of the numbers $0$ to $9$ with equal probability. Is it possible for you to design such a die? If so, please provide your design plan; if not, explain why.

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