
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 real numbers $a$ and $b$ satisfy $ab > 0$, and $a^2b = 4$. If $a + b \geq m$ always holds,  
(Ⅰ) Find the maximum value of $m$;  
(Ⅱ) If $2|x-1| + |x| \leq a + b$ holds for any $a$, $b$, find the range of the real number $x$.

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