
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
The sum to infinity of an infinite geometric progression is 6. The sum of the first two terms of the progression is $\frac{8}{3}$. Find the first term of the progression.
**A)** $6 + 2\sqrt{5}$  
**B)** $6 - 2\sqrt{5}$  
**C)** $6$  
**D)** $2\sqrt{5}$

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