
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 vertices of an isosceles triangle lie on the curve $xy=c^2$, where $c>0$ is a constant, and one vertex of the triangle is at the origin. The line of symmetry of the triangle is along the y-axis. If the triangle's altitude from the origin to the base is equal to 4 units, determine the length of each of the equal sides.

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