
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 $m \geq 0$, the function $f(x) = 2|x - 1| - |2x + m|$ has a maximum value of 3.
(Ⅰ) Find the value of the real number $m$;
(Ⅱ) If the real numbers $a$, $b$, and $c$ satisfy $a - 2b + c = m$, find the minimum value of $a^2 + b^2 + c^2$.

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