
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
If the center of the ellipse is at the origin, one of the foci is \\((0,2)\\), and the midpoint of the chord formed by the intersection of the line \\(y=3x+7\\) with the ellipse has a y-coordinate of \\(1\\), then the equation of this ellipse is \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_.

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