
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 $a$, $b$, $c \in \mathbb{R}$, and $a+b+c=3$, find the minimum value of $a^2+b^2+c^2$, denoted as $M$.  
(Ⅰ) Find the value of $M$;  
(Ⅱ) Solve the inequality $|x+4|-|x-1| \geq M$ with respect to $x$.

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