
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 $9$. The sum of the first two terms is $7$. The first term of the progression is:
A) $9$ or $9\sqrt{2}$
B) $3(3-\sqrt{2})$ and $3(3+\sqrt{2})$
C) $5$ or $11$
D) $3.5$ and $6.5$
E) $4$ or $8$

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