
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 functions $f(x)=ae^{x}-x+b$ and $g(x)=x-\\ln (x+1)$, where $a,b∈R$, and $e$ is the base of the natural logarithm. The tangent lines of the curves $y=f(x)$ and $y=g(x)$ at the coordinate origin are the same.

(1) Find the minimum value of $f(x)$;

(2) If $x\\geqslant 0$, find the range of the real number $k$ such that $f(x)\\geqslant kg(x)$ always holds.

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