
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
Points $A$, $B$, $C$, and $D$ lie on a line in that order with $AB=1$, $BC=2$, and $CD=3$. Points $E$, $F$, and $G$ lie on another line that is perpendicular to the first, with distances $EF=1$ and $FG=2$. A triangle with positive area has three of the seven points as its vertices. How many possible values are there for the area of the triangle?
A) 4
B) 5
C) 6
D) 7
E) 8

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