
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 points $A, B, C,$ and $D$ on a line with $AB=2$, $BC=1$, and $CD=3$, and points $E, F,$ and $G$ on a second line, parallel to the first, with $EF=1$ and $FG=2$, and the perpendicular distance between the two lines is a fixed, positive value $h$, determine the number of possible distinct areas that can be formed using any three of these seven points as vertices.

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