
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 school is holding a comprehensive knowledge competition, which consists of two parts: the preliminary round and the final round. The preliminary round is conducted in a manner where each contestant chooses one question to answer at a time, with a maximum of 6 opportunities to answer. A contestant's preliminary round ends if they answer 4 questions correctly or 3 questions incorrectly. Those who answer 4 questions correctly advance directly to the final round, while those who answer 3 questions incorrectly are eliminated. The probability of contestant A answering incorrectly two times in a row is $\frac{1}{9}$ (it is known that A's correct rate for each question is the same and that there is no influence among them).
(I) Calculate the probability of contestant A answering one question correctly.
(II) Calculate the probability of contestant A advancing to the final round.

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