
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 the equation \(2x^2-9x+8=0\), find a new quadratic equation such that one of its roots is the reciprocal of the sum of the roots of the original equation, and the other root is the square of the difference of the roots of the original equation.

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