
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
After being struck by a small stone, a glass pane cracked, creating four smaller triangles that share a common vertex at the point of impact. The following conditions are given:

- The glass pane was in the shape of a rectangle, which was $8 \mathrm{dm}$ wide and $6 \mathrm{dm}$ high,
- The triangle on the right has three times the area of the triangle on the left,
- The triangle on the left has half the area of the triangle at the bottom.

Determine the distances of the point of impact from the sides of the rectangle.

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