
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
During a school dance, a total of 430 different pairs danced. The first girl danced with 12 different boys, the second girl danced with 13 different boys, and so on, with the last girl dancing with all the boys. How many girls and boys attended the dance?

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