
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
The points $(2, 5), (10, 9)$, and $(6, m)$, where $m$ is an integer, are vertices of a triangle. What is the sum of the values of $m$ for which the area of the triangle is a minimum?

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