
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
Petya showed Vasya 37 identical-looking cards laid out in a row. He said that the hidden sides of the cards contain all the numbers from 1 to 37 (each exactly once) in such a way that the number on any card starting from the second one is a divisor of the sum of the numbers written on all the preceding cards. Then Petya revealed to Vasya that the number 37 is written on the first card and the number 1 is written on the second card. Vasya said that he then knows what number is written on the third card. What number is written on the third card?

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