
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
Distinct points $A$, $B$, $C$, $D$, and $G$ lie on a line, with $AB = 1$, $BC = 2$, $CD = 1$, $DG = 3$. Points $E$ and $F$ lie on a second line, parallel to the first, with $EF = 1$ and $F$ directly below $D$. Determine the number of possible values for the area of the triangle.

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