
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 that the graphs of functions f(x) and g(x) are symmetric about the origin, and f(x) = 2x + 1,

1. Solve the inequality g(x) ≥ |x - 1| for x.
2. If the inequality |g(x)| - c ≥ |x - 1| holds true for all x ∈ R, find the range of values for the real number c.

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