
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
Find a quadratic equation whose roots, $x$ and $y$, satisfy the conditions:
1. $x + y = 10$
2. $|x - y| = 4$
3. $xy = 21$
A) $x^2 - 10x + 24 = 0$
B) $x^2 - 7x + 21 = 0$
C) $x^2 - 10x + 21 = 0$
D) $x^2 - 10x - 21 = 0$
E) $x^2 + 10x + 21 = 0$

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