
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 ellipse is tangent to the y-axis at the origin. Given that the length of the major axis is 20 and one of the foci is at \((3,4)\), find the coordinates of the other focus.

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