
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 graph of $y=ax^2+bx+c$ ($a\neq 0$) intersects with the line $y=kx+4$ at points $A(1, m)$ and $B(4, 8)$, and intersects with the x-axis at the origin and point $C$.  
(1) Find the equations of the line and the parabola;  
(2) Is there a point $D$ on the parabola above the x-axis such that $S_{\triangle OCD}=2S_{\triangle OAB}$? If it exists, find the coordinates of point $D$, if not, explain why.

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