
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 Zircon encircles a star in an elliptical path, where the star is at one of the focus points. The closest point (perigee) of Zircon is 3 astronomical units (AU) from the star, and the farthest point (apogee) is 10 AU away. Determine the distance from Zircon to the star when it is midway along its orbit.

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