
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 $G$, $H$, $I$, and $J$ are collinear on a line with $GH = HI = IJ = 2$. Points $K$ and $L$ rest on another line, parallel to the first, and distanced such that $KL = 2$. Find the number of distinct possible values for the area of the triangle formed by any three of the six points.

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