
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
There is a dance with 42 participants. Lady \( A_{1} \) has danced with 7 male partners, Lady \( A_{2} \) has danced with 8 male partners, and so on... Lady \( A_{n} \) has danced with all the male partners. How many ladies and male partners are at the dance?

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