
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 distinct points $G$, $H$, $I$, and $J$ lie on a line, with $GH = HI = \frac{1}{2}$, and $IJ = 1$, and points $K$ and $L$ lie on a second line, parallel to the first, with $KL = 2$, determine the number of possible values for the area of a triangle formed by selecting any three of the six points.

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