
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

Let the function \\(f(x) = |x - a| + x\\), where \\(a > 0\\),

\\((1)\\) When \\(a = 1\\), find the solution set of the inequality \\(f(x) \geqslant x + 2\\);

\\((2)\\) If the solution set of the inequality \\(f(x) \leqslant 3x\\) is \\(\{x | x \geqslant 2\}\\), find the value of the real number \\(a\\).

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