
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 contest had $4200 available for prizes. The judging committee suggested awarding 7 prizes such that the 1st, 2nd, and 3rd prizes were to be $800, $700, and $300 respectively. How many people won the 1st prize, 2nd prize, and 3rd prize if the entire budget was allocated?

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