
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 5 yellow balls and 3 red balls. Balls are drawn from the bag, one at a time, and the color is recorded before the ball is returned to the bag. This process is repeated until a red ball has been drawn 10 times. If the random variable ξ represents the number of times balls are drawn when the process stops, find the probability that P(ξ=12).

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