
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
Planet Yvette orbits its sun in an elliptical path with the sun situated at one of the foci. The closest point of Yvette to its sun (perigee) is 3 astronomical units (AU), and its furthest point (apogee) is 15 AU away. Calculate the distance of Yvette from its sun when it is one-quarter way along its orbit from perigee towards apogee.

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