
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 the function $f(x) = x^2 + 2x$, and $g(x) + f(-x) = 0$.
1. Find the explicit expression for the function $g(x)$.
2. Solve the inequality $g(x) \ge f(x) - |x-1|$.
3. If the function $h(x) = g(x) - \lambda f(x) + 1$ is monotonically increasing on the interval $[-1, 1]$, find the range of the real number $\lambda$.

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