
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
a) Two seventh-grade students participated in a chess tournament along with some eighth-grade students. The two seventh-graders scored a total of 8 points, and each eighth-grader scored the same number of points. How many eighth-graders participated in the tournament? Find all possible solutions.

b) Ninth and tenth-grade students participated in a chess tournament. There were 10 times as many tenth-graders as ninth-graders, and they scored 4.5 times more points in total than all the ninth-graders. How many points did the ninth-graders score?

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