
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 inequality about $x$: $|2x-m| \leqslant 1$ has exactly one integer solution, which is $2$.
- (I) Find the value of the integer $m$;
- (II) Given $a$, $b$, $c \in \mathbb{R}$, if $4a^{4}+4b^{4}+4c^{4}=m$, find the maximum value of $a^{2}+b^{2}+c^{2}$.

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