
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
Let $a$ and $b$ be the roots of $k(x^2 - x) + x + 3 = 0.$ Find the values of $k$ for which $a$ and $b$ satisfy
\[
\frac{a}{b} + \frac{b}{a} = 2.
\]
Then, determine the sum of squares of these $k$ values.

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