
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 Zircon orbits its star in an elliptical path with the star located at one of the focusses. The closest Zircon gets to its star (perigee) is 3 astronomical units (AU) and its furthest distance (apogee) is 15 AU. Determine the distance from Zircon to its star when Zircon is halfway through its orbital path.

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