
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
Given the ellipse $\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1$, with $a > b > 0$, a line with a slope of $1$ intersects the ellipse at points $A$ and $B$. If the vector $\overrightarrow{OA} + \overrightarrow{OB}$ is collinear with the vector $\overrightarrow{a} = (3, -1)$, determine the eccentricity of the ellipse.

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