
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
Elective 4-5: Special Topics on Inequalities

Given the function \\(f(x) = |x-1| + |x-a|\\).

\\((1)\\) If \\(a \leqslant 2\\), solve the inequality \\(f(x) \geqslant 2\\).

\\((2)\\) If \\(a > 1\\) and \\(\forall x \in \mathbb{R}, f(x) + |x-1| \geqslant 1\\), find the range of the real number \\(a\\).

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