
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
A line $l: 2x - y + 2 = 0$ passes through the left focus $F\_1$ and a vertex $B$ of an ellipse. Determine the eccentricity of the ellipse.

A) $\frac{1}{5}$
B) $\frac{2}{5}$
C) $\frac{\sqrt{5}}{5}$
D) $\frac{2\sqrt{5}}{5}$

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