
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 Zephyr moves in an elliptical orbit with its star at one of the foci. At its nearest point (perihelion), it is 3 astronomical units (AU) from the star, while at its furthest point (aphelion) it is 15 AU away. Determine the distance of Zephyr from its star when it is exactly halfway through its orbit.

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