
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 there are three different points $A$, $B$, and $C$ on line $l_{1}$, where $2AB=BC=2$, and there are five different points $D$, $E$, $F$, $G$, and $H$ on line $l_{2}$, where $DE=EF=FG=GH=1$, $l_{1}$ is parallel to $l_{2}$, and the distance between $l_{1}$ and $l_{2}$ is $1$, find the number of triangles with an area of $1$ formed by these points.

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