
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 Ymir has an elliptical orbit around its star with the star at one focus. The nearest point of Ymir's orbit (perigee) is 3 astronomical units (AU) from the star, and the furthest point (apogee) is 15 AU away. Find the distance from Ymir to its star when Ymir is a quarter way along its orbit from the perigee.

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