
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 Zircon orbits its sun in an elliptical path with the sun at one of the foci. The nearest point of Zircon to its sun (perigee) is 3 astronomical units (AU) and its farthest point (apogee) is 15 AU. Determine how far Zircon is from its sun when it is one-fourth way from the perigee towards the apogee along its orbital path.

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