
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
B1 and B2 are the two endpoints of the minor axis of an ellipse, O is the center of the ellipse. A perpendicular line to the major axis is drawn from the left focus F1, intersecting the ellipse at P. If $|F1B2|$ is the geometric mean of $|OF1|$ and $|B1B2|$, then the value of \_\_\_\_\_\_\_\_.

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