
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 of which are red and the rest of which are yellow. When three balls are drawn at random at the same time, the probability that all three balls are red is $\frac{2}{91}$. Additionally, calculate the probability that all three balls are yellow if there are 6 more yellow balls than red balls.

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