
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
A computing device has a data input port (A) and an output port (B). According to a certain computational program:

1. When a natural number 1 is input from port A, the output from port B is 1/3, denoted as f(1)=1/3;
2. When a natural number n (n>=2) is input from port A, the result obtained from port B, f(n), is the (2(n-1)-1)/(2(n-1)+3) times of the previous result f(n-1).

(1) What numbers are obtained from port B when natural numbers 2, 3, 4 are input from port A respectively? And find the expression of f(n);
(2) Denote Sn as the sum of the first n terms of the sequence {f(n)}. When the reciprocal of 16112195 is obtained from port B, find the value of Sn at this time.

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