
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
In a jar, there are 5 salted duck eggs of the same size and shape, among which 3 have green shells, and 2 have white shells. If two eggs are taken out one after another without replacement, calculate:
(1) The probability of the first egg taken out being green-shelled;
(2) The probability that both the first and the second eggs taken out are green-shelled;
(3) Given that the first egg taken out is green-shelled, the probability that the second egg is also green-shelled.

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