
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
Elective 4-5: Selected Topics on Inequalities  
Given the function $$f(x)=(x-a)^{2}+(x-b)^{2}+(x-c)^{2}+ \frac {(a+b+c)^{2}}{3}$$ (where $a$, $b$, $c$ are real numbers), the minimum value of $f(x)$ is $m$. If $a-b+2c=3$, find the minimum value of $m$.

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