
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
Five students are seated in a circle, taking turns to count numbers in sequence. The rules are as follows: the first student says the number 1, the second student also says the number 1, and each subsequent student says a number that is the sum of the previous two students' numbers. If the number stated is a multiple of 3, the student must clap once. It is known that student A starts the counting.
(1) When the five students have taken turns counting a total of 20 numbers, the number of times student A claps is ______.
(2) By the time student A claps for the 10th time, these five students have taken turns counting up to the ______ number.

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