
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
Given that two students made individual mistakes in solving a quadratic equation, with one student getting roots $5$ and $3$ after erring in the constant term, and the other student getting roots $-7$ and $-2$ after erring in the coefficient of the first degree term, determine the correct equation for the quadratic.

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