
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
There are three brands, $A$, $B$, and $C$, of a certain type of beverage on the market, all of which are sold with prizes. It is known that the market shares of the three brands $A$, $B$, and $C$ are $60\%$, $30\%$, and $10\%$ respectively, and the winning rates per bottle for the three brands are $10\%$, $20\%$, and $30\%$ respectively. Now, if one bottle is purchased randomly from the market, the probability of winning a prize for that bottle is ____.

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