
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 > 0\\), \\(b > 0\\), and \\(a+b=1\\).
\\((1)\\) If \\(ab \leqslant m\\) always holds, find the range of \\(m\\);
\\((2)\\) If \\(\dfrac{1}{a} + \dfrac{1}{b} \geqslant |2x-1| - |x+1|\\) always holds, find the range of \\(x\\).

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