
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
On December 5th in the afternoon, our school solemnly held the 8th "Lü DaoKui Scholarship" award ceremony. All teachers of our school, the winners of the "Lü DaoKui Scholarship" in 2009, and nearly two thousand students attended this grand ceremony. Some parents of the students were also invited to attend. There were 27 outstanding graduates from the previous year and one ninth-grade student among the winners of this scholarship. Among them, each first-prize winner received 10,000 yuan, and each second-prize winner received 2,000 yuan, with the total prize money amounting to 80,000 yuan...
1. Do you know how many people won the first and second prizes, respectively? (Please solve by setting up equations or a system of equations)
2. After reading this report, how do you think you should study hard and strive for honors?

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