
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 function $f(x)=\frac{x}{x+1}$, define $f\_1(x)=f(x)$, $f\_2(x)=f\_1(f(x))$, $f\_3(x)=f\_2(f(x))$, ..., $f\_n(x)=f\_{n-1}(f(x))$ for $n \geq 2, n \in \mathbb{N}$. Find the value of $x$ such that $f\_{100}(x)=1$.

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