
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 inequality with respect to \\(x\\), \\(\left|x+1\right|+\left|2x-1\right|\leqslant 3\\), its solution set is \\(\{x|m\leqslant x\leqslant n\}\\).

\\((I)\\) Find the values of real numbers \\(m\\) and \\(n\\);

\\((II)\\) Let \\(a\\), \\(b\\), and \\(c\\) be positive numbers, and \\(a+b+c=n-m\\), find the minimum value of \\(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}\\).

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