
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
If the solution set of the inequality $|x+1|+|x-m|<5$ (where $m \in \mathbb{Z}$) is denoted as $A$, and $3 \in A$,  
(1) find the value of $m$  
(2) If $a, b, c \in \mathbb{R}$, and satisfy $a+2b+2c=m$, find the minimum value of $a^2+b^2+c^2$.

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