
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
Every high school in Plato City sent a team of 3 students to a national math competition. Charlie's score was the median among all the participants, also marking the highest score on his team. Charlie's teammates, Alice and Bob, secured the 45th and 58th positions respectively in terms of score. Determine the total number of high schools in Plato City.

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