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

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