
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
Consider the quadratic equation $k(x^2 - x) + 2x + 7 = 0$. Let $a$ and $b$ be the roots of this equation for which $\frac{a}{b} + \frac{b}{a} = 3$. Let $k_1$ and $k_2$ be the values of $k$ fulfilling the previous condition. Determine the value of $\frac{k_1}{k_2} + \frac{k_2}{k_1}$.

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