
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 standing in a circle, taking turns to count in sequence. The rules are as follows: 
1. The first student starts with the number 1, and the second student also starts with the number 1. Afterwards, each student announces a number that is the sum of the two previous numbers reported.
2. If the announced number is a multiple of 3, the student must clap once.

Knowing that student A is the first to count, by the time the students have sequentially counted up to the 100th number, student A has clapped a total of __________ times.

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