
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
Blind boxes are a new type of product. Merchants package different styles of products from the same series in boxes with the same appearance, so that consumers do not know which style of product they are buying. A merchant has designed three types of dolls, $A$, $B$, and $C$, in the same series, and sells them in blind boxes. It is known that the production ratio of the three types of dolls $A$, $B$, and $C$ is $6:3:1$. Using frequency to estimate probability, calculate the probability that a consumer randomly buys $4$ blind boxes at once and finds all three types of dolls inside.

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