
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
An equilateral triangle has an area of \( A \). A new triangle is formed by joining the midpoints of the sides of the first one. This process is repeated indefinitely. What is the sum of the areas of all these equilateral triangles?
**A)** \( \frac{2A}{3} \)  
**B)** \( \frac{4A}{3} \)  
**C)** \( \frac{A}{2} \)  
**D)** \( 2A \)  
**E)** \( A \)

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