
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 Yendor follows an elliptical orbit with its sun, Solara, at one focus. At its closest approach (perigee), Yendor is 3 astronomical units (AU) from Solara, while at its farthest point (apogee) it is 15 AU away. Yendor's orbit also contains another celestial body, Lunaris, exactly at the second focus. Calculate the distances from Yendor to Solara and Lunaris when Yendor is midway along its orbit, in AU.

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