
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 a line \\(l_{1}\\) passing through the point \\((2,0)\\) intersects the parabola \\(C\\): \\(y^{2}=2px\\) at points \\(A\\) and \\(B\\), and the line \\(l_{2}\\): \\(x=-2\\) intersects the \\(x\\)-axis at point \\(Q\).
\\((1)\\) Let the slopes of lines \\(QA\\) and \\(QB\\) be \\(k_{1}\\) and \\(k_{2}\\) respectively, find the value of \\(k_{1}+k_{2}\\);
\\((2)\\) Let point \\(P\\) be any point on the parabola \\(C\\) other than points \\(A\\) and \\(B\\), lines \\(PA\\) and \\(PB\\) intersect line \\(l_{2}\\) at points \\(M\\) and \\(N\\) respectively, and \\(\overrightarrow{OM} \cdot \overrightarrow{ON}=2\\), find the equation of the parabola \\(C\\).

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