
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
Consider planet Zephyr which orbits in an elliptical path around its sun, located at one focus of the ellipse. The closest point of orbit (perigee) is 3 astronomical units (AU) from its sun, and its farthest point (apogee) is 15 AU away. Calculate the distance of Zephyr from the sun when it is vertically above the center of the ellipse in its orbit.

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