
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
A comet follows an elliptical orbit around a star with the star situated at one focus. At its closest approach (perihelion), the comet is 3 astronomical units (AU) from the star, and at its farthest point (aphelion), it is 15 AU away. Calculate the distance of the comet from the star when it is exactly halfway along its orbit.

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