
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 an ellipse $C: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \ (a > b > 0)$ with an eccentricity of $\frac{\sqrt{2}}{2}$, and the minimum distance from a point on the ellipse to the left focus $F_1$ of the ellipse $C$ is $\sqrt{2} - 1$.

1. Find the equation of $C$.
2. If $B_2$ is the top vertex and $F_2$ is the right focus, find the degree measure of $\angle B_2F_1F_2$.

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