
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 two functions $f(x)$ and $g(x)$, which are defined on the set $D$, and where $|f(x) - g(x)| \leq 1$ for any $x \in D$, if $f(x) = x^2 + 3x + 2$ and $g(x) = 2x + 3$ are fate functions over the interval $[a, b]$, determine the fate region $D$.

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