
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
Consider the function $f(x)= \frac{x}{x+1}$ for $x > 0$. Observe the following: 
$$f_{1}(x)=f(x)= \frac{x}{x+1},$$ 
$$f_{2}(x)=f(f_{1}(x))= \frac{x}{2x+1},$$ 
$$f_{3}(x)=f(f_{2}(x))= \frac{x}{3x+1},$$ 
$$f_{4}(x)=f(f_{3}(x))= \frac{x}{4x+1}.$$ 
Based on these observations, we can infer by induction that for $n \in \mathbb{N}^{+}$ and $n \geq 2$, the function $f_{n}(x) = f(f_{n-1}(x)) = \_\_\_\_\_\_$.

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