
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 \\(a \in (0, +\infty)\\) and \\(b \in (0, +\infty)\\) with \\(a + b = 2\\),
\\((1)\\) Find the minimum value of \\( \dfrac {1}{a} + \dfrac {4}{b}\\);
\\((2)\\) If for all \\(a\\), \\(b \in (0, +\infty)\\), \\( \dfrac {1}{a} + \dfrac {4}{b} \geqslant |2x-1| - |x+1|\\) always holds, find the range of the real number \\(x\\).

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