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

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