
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
From the set of positive integers \\(1,2,3,\cdots,n\\), two different numbers are randomly selected. If the probability that the sum of these two numbers equals \\(7\\) is \\(\dfrac{3}{28}\\),

(Ⅰ) find the value of \\(n\\);

(Ⅱ) If \\({(1-2x)}^{n} = {a_0} + {a_1}x + {a_2}{x^2} + \cdots + {a_n}{x^n}\\),

  ① find the value of \\({a_3}\\);

  ② when selecting any three different elements from \\(\left(a_0,a_1,a_2,a_3,\cdots,a_n\right)\\), find the probability that the product of these three elements is negative.

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