
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 \\(l:\\begin{cases} & x=1+\\dfrac{1}{2}t \\\\ & y=\\dfrac{\\sqrt{3}}{2}t \\\\ \\end{cases}(t\\) as the parameter\\()\\), and the curve \\({{C}\_{1}}:\\begin{cases} & x=\\cos \\theta \\\\ & y=\\sin \\theta \\\\ \\end{cases}(θ \\) as the parameter\\()\\).

\\((\\)Ⅰ\\()\\) Suppose \\(l\\) intersects \\({{C}\_{1}}\\) at points \\(A,B\\), find \\(|AB|\\);

\\((\\)Ⅱ\\()\\) If the x-coordinates of the points on curve \\({{C}\_{1}}\\) are compressed to half of their original values, and the y-coordinates are compressed to \\(\\dfrac{\\sqrt{3}}{2}\\) of their original values, resulting in curve \\({{C}\_{2}}\\), let point \\(P\\) be a moving point on curve \\({{C}\_{2}}\\), find the minimum distance from it to the line \\(l\\).

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