
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 the functions $f(x)$ and $g(x)$ are symmetric about the origin, and $f(x) = x^2 + 2x$.

(Ⅰ) Solve the inequality $g(x) \geq f(x) - |x-1|$;

(Ⅱ) If for $\forall x \in \mathbb{R}$, the inequality $g(x) + c \leq f(x) - |x-1|$ always holds, find the range of the real number $c$.

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