
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 university graduate participates in a recruitment exam at an organization, which consists of three consecutive rounds: a written test, an interview, and a practical test. To continue to the next round, candidates must pass the current one. Only those who pass all three rounds will be officially employed. The probabilities for the graduate to pass the first, second, and third rounds are $\frac{2}{3}$, $\frac{3}{4}$, and $\frac{4}{5}$ respectively, with each round's outcome being independent of the others.

1. Calculate the probability of the graduate making it to the third round.
2. Let X represent the number of rounds the graduate participates in during the recruitment process. Determine the probability distribution, the expected value, and the variance of X.

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