
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 a triangle ABC where $A = (1,3)$, $B = (1,0)$, and $C = (10,0)$, a vertical line $x = a$ divides the triangle into two regions. The area of the region on the left of the line $x = a$ is three times the area of the region on the right. Determine the value of $a$.
A) $x = 6.75$
B) $x = 7.00$
C) $x = 7.75$
D) $x = 8.00$

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