
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 the equation $5x^2 - 10x + m = 0$, find the value of $m$ for which the sum of the square of the roots is minimized, given that the roots are real.
A) $m = 2$
B) $m = \frac{8}{5}$
C) $m = 3$
D) $m = 5$

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