
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 30 rubles, and a fountain pen costs 60 rubles. What is the maximum number of ballpoint pens that can be bought under the condition that a total of exactly 20 pens must be bought, including pens of all three types, and exactly 500 rubles must be spent?

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