
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 box contains twelve balls, some of which are blue and the rest of which are green. When two balls are drawn at random at the same time, the probability that both balls are blue is $\frac{1}{22}$. How many balls in the box are blue?

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