
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 that O is the origin, there exists a point P(x_{0},y_{0}) ($x_{0} \in (0,e-1)$) on the curve $f(x)=a\ln (x+1)-x-b$, satisfying two conditions: 
1. The line OP is the tangent line of the curve f(x);
2. The line OP is perpendicular to a tangent line l of the curve g(x)=e^{x} passing through the origin. Determine the range of the real number b.

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