
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 fifteen balls: some are red, some are yellow, and the rest are blue. If two balls are drawn at random at the same time, and the probability that neither of those balls are red is $\frac{2}{7}$, find out how many red balls are in the bag.

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