
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
Catarina has 210 cards numbered from 1 to 210.

a) How many of these cards have a number that is a multiple of 3?

b) How many of these cards have an even number that is not a multiple of 3?

c) What is the minimum number of cards Catarina must randomly pick to be sure that at least two of them have the numbers 2 or 3 as a common divisor?

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