
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 that David's score was the median among all students and his was the highest score on his team, and David's teammates Ellen and Frank placed 29th and 50th, respectively, determine the number of schools in the city of Pythagoras.

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