
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
A jar contains 12 balls, some of which are blue and the rest are green. When three balls are drawn at random at the same time, the probability that all three balls are blue is $\frac{1}{55}$. How many balls in the jar are blue?

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