
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
A ballpoint pen costs 10 rubles, a gel pen costs 40 rubles, and a fountain pen costs 60 rubles. What is the maximum number of ballpoint pens that can be bought given that exactly 15 pens must be purchased in total, including at least one of each type, and the total expenditure must be exactly 500 rubles?

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