
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 $f(x)= \begin{cases} \ln (x+1) & (x\geqslant 0)\\ 2^{-x}-1 & (x < 0) \end{cases}$. If a real number $x_{0}$ is randomly selected from the interval $[-e,e]$, and $A$ represents the event "$f(x_{0})\leqslant 1$", calculate the probability $P(A)$.

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