
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
The planet Zenon follows an elliptical orbit around its star with the star at one focus. At its closest approach (perigee), Zenon is 3 astronomical units (AU) from the star, and at its farthest point (apogee), it is 15 AU away. Calculate how far Zenon is from its star when it is at one vertex of the minor axis of its orbit.

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