
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 functions $f(x)=|x-1|-1$ and $g(x)=-|x+1|-4$.
1. Find the range of $x$ for which the value of function $f(x)$ does not exceed $1$.
2. If the solution set of the inequality $f(x)-g(x)\geq m+1$ is $R$, find the range of $m$.

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