
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
In a bag, there are 5 white balls and 3 red balls. Balls are drawn one at a time from the bag, the color is recorded, and then the ball is placed back into the bag. This process continues until a red ball has been drawn 10 times. Let $X$ be the random variable representing the number of draws when the process stops. Calculate $P(X=12)$ (Answer with an expression).

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