
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 Yolara follows an elliptical path around its star, with the star situated at one focus of the ellipse. At its nearest point (perigee), Yolara is 3 astronomical units (AU) away from the star, and at its furthest point (apogee), it is 8 AU away. Determine Yolara's distance from its star when it is one-fourth of the way from perigee to apogee.

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