
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 the series \(3 + 2 + \frac{2}{3} + \frac{2}{9} + \cdots\) and the following statements:

(1) The sum increases without limit.  
(2) The sum decreases without limit.  
(3) The difference between any term of the sequence and zero can be made less than any positive quantity no matter how small.  
(4) The difference between the sum and 6 can be made less than any positive quantity no matter how small.  
(5) The sum approaches a limit.

Of these statements, the correct ones are:
**A)** Only 3  
**B)** Only 5  
**C)** Only 3 and 5  
**D)** Only 2, 3, and 4  
**E)** Only 1 and 4

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