
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 \(a, b,\) and \(c\) are all non-zero, and

\[ 
a + b + c = m, \quad a^2 + b^2 + c^2 = \frac{m^2}{2},
\]

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