
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
In a checkers tournament, students from 10th and 11th grades participated. Each player played against every other player exactly once. A win earned a player 2 points, a draw earned 1 point, and a loss earned 0 points. The number of 11th graders was 10 times the number of 10th graders, and together they scored 4.5 times more points than all the 10th graders combined. How many points did the most successful 10th grader score?

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