
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 Yavin moves in an elliptical orbit around its star. At its closest approach, called perigee, it is 3 astronomical units (AU) from the star. At its farthest point, known as apogee, it is 15 AU away. Determine how far Yavin is from its star when it is exactly halfway through its orbit. Additionally, calculate the length of the semi-minor axis of Yavin's orbit.

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