
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 $m(x^2 - 2x) + 3x + 7 = 0.$ Let $m_1$ and $m_2$ be the values of $m$ for which $a$ and $b$ satisfy
\[\frac{a}{b} + \frac{b}{a} = \frac{7}{10}.\] Find
\[\frac{m_1}{m_2} + \frac{m_2}{m_1}.\]

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