
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
Consider a triangle with vertices at points \(A = (1, 3)\), \(B = (1, 1)\), and \(C = (10, 1)\). Calculate the y-coordinate, \(y = b\), of a horizontal line that divides the triangle into two regions, each having an equal area.
A) \(b = 1.5\)
B) \(b = 2\)
C) \(b = 2.5\)
D) \(b = 3\)

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