
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 $f(x) = |x-3| - 2$ and $g(x) = -|x+1| + 4$. If the solution set for $f(x) - g(x) \geq m + 1$ is $\mathbb{R}$, determine the range of values for $m$.

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