
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
There is a bag containing 8 white balls and 2 red balls. Each time a ball is randomly taken out, and then a white ball is put back into the bag. What is the probability that all red balls have been taken out exactly after the 4th draw?

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