
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 G, H, I, and J lie on a line, with GH = 2, HI = 3, IJ = 4, and points K, L, and M lie on another line, parallel to the first, with KL = 2 and LM = 3, determine the number of possible different values for the area of a triangle with positive area formed by three of these points.

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