
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
In a convex quadrilateral $ABCD$, $M$ and $N$ are the midpoints of sides $AD$ and $BC$, respectively. Given that $|\overrightarrow{AB}|=2$, $|\overrightarrow{MN}|=\frac{3}{2}$, and $\overrightarrow{MN} \cdot (\overrightarrow{AD} - \overrightarrow{BC}) = \frac{3}{2}$, find $\overrightarrow{AB} \cdot \overrightarrow{CD}$.

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