
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
The ellipse \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 \ (a > b > 0)\) has an eccentricity of \(\frac{\sqrt{3}}{2}\). A line with a slope of 1 that passes through point \(M(b, 0)\) intersects the ellipse at points \(A\) and \(B\). Let \(O\) be the origin, and it is given that \(\overrightarrow{OA} \cdot \overrightarrow{OB} = \frac{32}{5} \cot \angle AOB\). Determine the equation of the ellipse.

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