
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
In the dance ensemble, there are 8 boys and 20 girls. Some of them form mixed (a boy and a girl) dance pairs. It is known that in each pair at least one of the partners is not part of any other pair. What could be the maximum number of dance pairs in this ensemble?

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