
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 that the real numbers \(a, b, c\) are all non-zero, and \(a+b+c=m\) and \(a^{2}+b^{2}+c^{2}=\frac{m^{2}}{2}\), find the value of \(\frac{a(m-2a)^{2}+b(m-2b)^{2}+c(m-2c)^{2}}{abc}\).

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