
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 the terms of an infinite geometric progression is $10$. The sum of the first two terms is $7$. Find the first term of the progression.
A) \(10\left(1 - \sqrt{\frac{3}{10}}\right)\)  
B) \(10\left(1 + \sqrt{\frac{3}{10}}\right)\)  
C) \(5 + 5\sqrt{\frac{3}{10}}\)  
D) \(7\)

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