
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
From a point $P$ on the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ where $a > b > 0$, a perpendicular line is drawn to the $x$-axis, and the foot of the perpendicular is exactly the left focus $F_1$. $A$ is the intersection point of the ellipse with the positive $x$-axis, and $B$ is the intersection point of the ellipse with the positive $y$-axis, and $AB$ is parallel to $OP$ ($O$ is the origin). Given that $\angle OF_1 PF_2$ is a right angle, calculate the eccentricity of the ellipse.

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