
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 \\(F_{1}\\) and \\(F_{2}\\) are the left and right foci of the ellipse \\(C\\): \\( \dfrac {x^{2}}{8}+ \dfrac {y^{2}}{2}=1\\), and point \\(P(x_{0},y_{0})\\) is on the ellipse \\(C\\).
\\((\\)Ⅰ\\()\\) Find the minimum value of \\( \overrightarrow{PF_{1}}\cdot \overrightarrow{PF_{2}}\\);
\\((\\)Ⅱ\\()\\) Suppose the slope of line \\(l\\) is \\( \dfrac {1}{2}\\), and line \\(l\\) intersects the ellipse \\(C\\) at points \\(A\\) and \\(B\\). If point \\(P\\) is in the first quadrant and \\( \overrightarrow{PF_{1}}\cdot \overrightarrow{PF_{2}}=-1\\), find the maximum value of the area of \\(\triangle ABP\\).

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