
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 \( f(x)=\left\{\begin{array}{l}2^{-x}-1, x \leqslant 0, \\ f(x-1), x>0,\end{array}\right. \), if the equation \( f(x)=x+a \) has exactly two distinct real roots, then the range of the real number \( a \) is ______.

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