
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 function $f(x)=|x-m|$, the solution set of the inequality $f(x)\leqslant 3$ with respect to $x$ is $[-1,5]$.

(I) Find the value of the real number $m$;

(II) If the real numbers $a,b,c$ 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