
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
The numbers 1 through 30 are written on 30 cards with one number on each card. Sara and Tom take turns picking one of the 30 cards at random. What is the probability that the number on the card picked by Sara would be a multiple of 3? And what is the probability that the number on Tom's card, picked immediately after Sara's pick, will be an odd number? Express your answer as a reduced fraction.

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