
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
$f(x) = |x-3| - 2$, $g(x) = 4 - |x+1|$

(Ⅰ) If $f(x) \geq g(x)$, find the range of $x$.

(Ⅱ) If the solution set of the inequality $f(x) - g(x) \geq a^2 - 3a$ is $\mathbb{R}$, find the range of the real number $a$.

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