
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
Let the function be defined as $$f(x)= \frac {x}{x+2} \quad (x＞0)$$, observe: $$f_{1}(x)=f(x)= \frac {x}{x+2}$$, $$f_{2}(x)=f(f_{1}(x))= \frac {x}{3x+4}$$, $$f_{3}(x)=f(f_{2}(x))= \frac {x}{7x+8}$$, $$f_{4}(x)=f(f_{3}(x))= \frac {x}{15x+16}$$, …, according to the above facts, when $n\in\mathbb{N}^{*}$, by inductive reasoning, we can obtain: $f_{n}(1)=$ \_\_\_\_\_\_.

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