
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 case contains 20 cassette tapes with disco music and 10 with techno music. A DJ randomly picks two tapes one after the other. What is the probability that
1) The first tape contains disco music;
2) The second tape also contains disco music.

Consider two scenarios:
a) The DJ returns the first tape to the case before picking the second tape;
b) The DJ does not return the first tape to the case.

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