
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
A triangle has vertices at $(0,0)$, $(4,4)$, and $(10m,0)$, and the line $y = mx$ divides the triangle into two triangles of equal area. Calculate the sum of all possible values of $m$.
$\textbf{A} -0.6 \qquad \textbf{B} -0.4 \qquad \textbf{C} 0.4 \qquad \textbf{D} 0.6 \qquad \textbf{E} None of the above$

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