
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
Consider the planet Krypton which orbits its sun in an elliptical path with the sun at one of its foci. At its closest approach (perigee), Krypton is 3 astronomical units (AU) from the sun, and at its farthest point (apogee), it is 9 AU away. Calculate the distance from the sun to Krypton when Krypton is one quarter of the way along the ellipse from the perigee towards the apogee.

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