
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
29 boys and 15 girls came to the ball. Some boys danced with some girls (no more than once per pair). After the ball, each person told their parents how many times they danced. What is the greatest number of distinct counts that the children could report?

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