
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 inequality about $x$, $m - |x - 2| \geq 1$, its solution set is $[0, 4]$.
(Ⅰ) Find the value of $m$;
(Ⅱ) If $a$ and $b$ are both positive real numbers, and satisfy $a + b = m$, find the minimum value of $a^2 + b^2$.

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