
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
I have 10 identical balls, one of which is radioactive, but I don't know which one. A friend would buy only non-radioactive balls from me for 1 forint each. Another friend has an instrument that can determine whether any number of balls include a radioactive one. He charges 1 forint per measurement, but if there is a radioactive ball among the measured balls, all of them become radioactive during the measurement. What is the maximum profit I can guarantee?

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