
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
We construct a triangle using the midlines of triangle $ABC$ as its sides; then, using the midlines of this new triangle, we construct another triangle, and so on, infinitely. What is the sum of the areas of all these triangles if the area of the original triangle is $t$?

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