
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 that distinct points $A$, $B$, $C$, and $D$ lie on a line, with $AB=1$, $BC=2$, and $CD=3$, and points $E$ and $F$ lie on a second line, parallel to the first, with $EF=2$, determine the number of possible values for the area of a triangle with positive area formed from three of the six points.

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