
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
Given 4 students from each school, with Andrea's being the highest score of her team and the median of all students, and Beth and Carla placing 39th and 65th, respectively, calculate the number of schools in the city of Pythagoras.

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