
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 analytical expression of function $g(x)$;
2. Solve the inequality $g(x)\geqslant f(x)-|x-1|$;
3. If $h(x)=g(x)-λf(x)+1$ is monotonically increasing on $[-l,1]$, find the range of the real number $λ$.

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