
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 line $y=kx+1$ ($k\neq 0$) intersects the parabola $x^2=4y$ at points E and F, and the chord length intercepted by the circle with diameter EF on the x-axis is $2\sqrt {7}$, find the value of $k$.

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