
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 $6$ white balls and $3$ red balls. Balls are drawn from the bag one at a time, with the color of each ball recorded before it is returned to the bag. This process continues until a red ball has been drawn $9$ times. Let $X$ be the random variable representing the number of draws when this process stops. Find the value of $P(X=11)$.

A) $C_{11}^{9}(\frac{1}{3})^{8}\cdot(\frac{2}{3})^{3}$
B) $C_{10}^{8}(\frac{1}{3})^{8}\cdot(\frac{2}{3})^{2}$
C) $C_{10}^{8}(\frac{1}{3})^{9}\cdot(\frac{2}{3})^{2}$
D) $(\frac{1}{3})^{8}\cdot(\frac{2}{3})^{3}$

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