
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
Planet Xenon orbits its star in an elliptical path with the star located at one of the foci. The closest point of Xenon to its star is 3 AU (at perigee), and the farthest point is 15 AU (at apogee). Calculate the distance of Xenon from its star when Xenon is one-fourth the way from perigee to apogee along the major axis of its orbit.

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