
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 graduation exam, a benefactor distributed rewards among the top students in such a way that the top-ranked student received a certain amount, the next received slightly less than the first, the third received the same amount less than the second, and so on. However, the fifth-ranked student was absent and the third-ranked student received the rewards for both themselves and the fifth-ranked student, totaling 40 forints. Additionally, the ninth-ranked student was also absent, and their reward was given to the sixth-ranked student, who received a total of 30 forints for both their own and the ninth's share. What were the rewards for the students ranked 3rd, 5th, 6th, and 9th?

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