
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 quadratic equation $2x^2 - 5x + m = 0$ with real roots, find the value of $m$ for which the sum of the roots of the equation is a maximum.
**A)** $\frac{25}{8}$  
**B)** $\frac{31}{8}$  
**C)** $\frac{5}{2}$  
**D)** $\frac{19}{8}$

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