
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 that the center of the ellipse is the origin, the major axis \\(AB\\) is on the \\(x\\)-axis, and point \\(C\\) is on the ellipse with \\(∠CBA= \dfrac {π}{4}\\). If \\(AB=4\\) and \\(BC= \sqrt {2}\\), then the equation of the ellipse is \_\_\_\_\_\_.

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