
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 television station is holding an Olympic knowledge quiz show, which is divided into a preliminary round and a final round. To make the show more interesting, the preliminary round allows contestants to choose a question and answer it, with each contestant having up to 5 opportunities to choose and answer questions. The preliminary round ends for a contestant once they have answered 3 questions correctly or incorrectly. Those who answer 3 questions correctly go directly to the final, while those who answer 3 questions incorrectly are eliminated. It is known that the probability of contestant A answering a question correctly is $$\frac{2}{3}$$.
(Ⅰ) Calculate the probability that contestant A will make it to the final round;
(Ⅱ) Let $\xi$ be the number of questions contestant A answers in the preliminary round. Write the distribution of $\xi$ and calculate its expected value.

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