
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
Given the parabola C<sub>1</sub> with the equation $y = \frac{1}{20}x^2$, the point symmetric to its focus F with respect to the origin is E. If the absolute value of the difference in distances from a point on curve C<sub>2</sub> to points E and F equals 6, then the standard equation of curve C<sub>2</sub> is __________.

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