
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
When Buratino went to VMSH classes, Papa Carlo promised to pay him one kopek for the first correctly solved problem, two kopeks for the second, four kopeks for the third, and so on. In a month, Buratino received 655 rubles and 35 kopeks. How many problems did he solve?

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