
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
Solve the application problem by setting up equations. In the book "Nine Chapters on the Mathematical Art," there is a problem called "Deficiency and Excess." The original text is as follows: "Suppose a group of people jointly buy sheep. If each person contributes $5, there will be a shortage of $45; if each person contributes $7, there will be a shortage of $3. How many people and what is the price of each sheep?"

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