
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 Yalgeth follows an elliptical orbit with its sun at one focus. At its nearest point (perigee), it is 5 astronomical units (AU) from the sun, while at its furthest point (apogee) it is 20 AU away. Calculate the distance of Yalgeth from the sun when it is at a true anomaly of \(90^\circ\), which is the point directly perpendicular from the perigee along the orbit.

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