
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 every high school in the town of Pythagoras sent a team of 3 students to a math contest, and Andrea's score was the median among all students, and hers was the highest score on her team, and Andrea's teammates Beth and Carla placed 40th and 75th, respectively, calculate the number of schools in the town.

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