
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 the equation $m(x^2 - 3x) + 2x + 7 = 0$. Let $m_1$ and $m_2$ be the values of $m$ for which $p$ and $q$ satisfy
\[\frac{p}{q} + \frac{q}{p} = 2.\] Find
\[\frac{m_1}{m_2} + \frac{m_2}{m_1}.\]

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