
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
(1) Let the function $$f(x)=| \frac {1}{2}x+1|+|x| \quad (x \in \mathbb{R})$$. Find the minimum value of $f(x)$.

(2) Given $a+2b+3c=m$ ($a, b, c \in \mathbb{R}$), find the minimum value of $a^2+b^2+c^2$.

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