
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 $f(x)= \begin{cases}2^{x}-1,x\leqslant 0 \\ f(x-1)+1,x > 0\end{cases}$, let $s_{n}$ be the sum of all real roots of the equation $f(x)=x$ in the interval $(0,n]$. Then the sum of the first $n$ terms of the sequence $\{\frac{1}{s_{n}}\}$, denoted as $T_{n}$, is \_\_\_\_\_\_.

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