
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
In a lottery machine, there are 10 balls, among which 8 balls are marked with the number 2, and 2 balls are marked with the number 5. Now, if 3 balls are drawn, the prize money (in yuan) is determined by the sum of the numbers on these balls. If you participate in this lottery, find all possible prize amounts and their corresponding probabilities.

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