
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
In the xy-plane, let triangle ABC be defined with vertices at A = (0,4), B = (0,0), and C = (10,0). A vertical line, x = k, is drawn from the x-axis upwards, and it divides triangle ABC into two regions of equal area. Find the value of k.
A) 3
B) 5
C) 7
D) 9

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