
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
Let the function \\(f(x) = |ax + 1| + |x - a|\\) where \\(a > 0\\), and \\(g(x) = x^2 + x\\).
\\((1)\\) When \\(a = 1\\), find the solution set of the inequality \\(g(x) \geqslant f(x)\\).
\\((2)\\) Given that \\(f(x) \geqslant \frac{3}{2}\\), find the range of values for \\(a\\).

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