
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 the pole \\(O\\) of the polar coordinate system coincides with the origin of the Cartesian coordinate system, and the polar axis coincides with the positive half-axis of the \\(x\\)-axis in the Cartesian coordinate system. The parametric equation of circle \\(C\\) is \\( \begin{cases} x=a+a\cos θ \\ y=a\sin θ\end{cases} (θ\\) is the parameter, \\(0 < a < 5)\\), and the line \\(l\\): \\(ρ\sin (θ+ \dfrac {π}{4})=2 \sqrt {2}\\). If line \\(l\\) intersects curve \\(C\\) at points \\(A\\) and \\(B\\), and \\(|AB|=2 \sqrt {2}\\).
\\((\\)Ⅰ\\()\\) Find \\(a\\);
\\((\\)Ⅱ\\()\\) If \\(M\\) and \\(N\\) are two points on curve \\(C\\), and \\(∠MON= \dfrac {π}{3}\\), find the minimum value of \\(|OM|+|ON|\\).

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