
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
The prize for the team award in a math competition is 10,000 math extracurricular books. The prizes are distributed to the schools of the top five teams. The teams with higher rankings receive more books, and the number of books for each ranking is a multiple of 100. If the number of books awarded to the first-place team is equal to the sum of the books awarded to the second and third-place teams, and the number of books awarded to the second-place team is equal to the sum of the books awarded to the fourth and fifth-place teams, then the third-place team can receive at most _ books.

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