
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 ellipse \\(C: x^2 + 2y^2 = 4\\), and the line \\(l: y = 2x + t\\) intersects the ellipse \\(C\\) at two distinct points \\(A\\) and \\(B\\), then the equation of the trajectory of the midpoint of segment \\(AB\\) is ______________.

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