
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 $f(x) = e^{x} + a\sin x + b$.

(1) When $a=1$ and $x\in [0,+\infty)$, $f(x)\geqslant 0$ always holds. Find the range of $b$.

(2) If the tangent line of $f(x)$ at $x=0$ is $x-y-1=0$, and the equation $f(x) = \dfrac{m-2x}{x}$ has exactly two solutions, find the range of the real number $m$.

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