
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
The integer solution for the inequality $|2x-m|\leq1$ with respect to $x$ is uniquely $3$ ($m$ is an integer).
(I) Find the value of the integer $m$;
(II) Given that $a, b, c \in R$, 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