
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 A and an operation output B, performing a certain operation program.
(1) When the natural number 1 is input from port A, the real number $\frac{1}{3}$ is obtained from port B, denoted as $f(1) = \frac{1}{3}$;
(2) When the natural number $n$ ($n \geq 2$) is input from port A, the result $f(n)$ obtained from port B is $\frac{2(n-1)-1}{2(n-1)+3}$ times the previous result $f(n-1)$.
To obtain $\frac{1}{1443}$ from port B, the natural number that should be input from port A is \_\_\_\_\_\_.

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