
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
Let the function $f(x) = \sqrt{2x-4} + \sqrt{5-x}$ have a maximum value of $M$.  
(Ⅰ) Find the value of the real number $M$;  
(Ⅱ) Find the solution set of the inequality $|x-1|+|x+2| \leq M$ with respect to $x$.

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