
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 Zytron orbits in an elliptical path around its star with the star located at one of the foci of the ellipse. Zytron’s closest approach to its star (perihelion) is 3 astronomical units (AU), and its furthest point (aphelion) is 8 AU away. How far is Zytron from its star when it is exactly halfway in its orbit along the major axis?

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