
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 two lines intersecting in the coordinate plane, defined by two distinct sets of points. Line 1 is determined by the points (0,3) and (6,0), and Line 2 is defined by the points (1,6) and (7,1). Find the area of the triangular region formed by the intersection of these two lines and the x-axis.
A) 8
B) 8.5
C) 9
D) 9.5
E) 10

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