
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
The quadratic equation \( a x^{2} + b x + c = 0 \) has two roots. Formulate a new quadratic equation where one root is one unit less than the larger root, and the other root is one unit more than the smaller root of the given equation.

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