
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 quadratic expression $ax^2 + bx + c$ has coefficients $a$, $b$, and $c$, and two roots $x_{1}$ and $x_{2}$. These five quantities (the three coefficients and two roots) are written in some order as five consecutive integers. Find all such quadratic expressions, and briefly explain the reasoning process.

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