
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 a triangle \( T \) with an area of 1, \( T_{1} \) is the medial triangle of \( T \), whose vertices are the midpoints of sides of \( T \). Then \( T_{2} \) is the medial triangle of \( T_{1} \), \( T_{3} \) is the medial triangle of \( T_{2} \), and so on. What is the sum of the areas of \( T_{1}, T_{2}, T_{3}, T_{4}, \ldots \)?

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