
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 conference of doctors was held in the city. Four doctors were invited from each clinic. Each of the invited doctors worked in two clinics and represented both clinics at the conference. Any possible combination of two clinics had exactly one representative at the conference. How many clinics are there in the city? How many doctors were invited to the conference?

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