
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 $p$ and $q$ be the roots of $k(x^2 - 2x) + 3x + 7 = 0.$ Let $k_1$ and $k_2$ be the values of $k$ for which $p$ and $q$ satisfy
\[\frac{p}{q} + \frac{q}{p} = \frac{6}{7}.\] Find
\[\frac{k_1}{k_2} + \frac{k_2}{k_1}.\]

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