
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 $f(x)=e^{x}$ and $g(x)=kx+1$, the graph of the function $y=f(x)$ is tangent to the line $y=g(x)$.

1. Find the value of the real number $k$.
2. Let $h(x)=f(x)-g(x)$. If the inequality $(m-x)h′(x) < x+1$ holds for any $x∈(0,+∞)$ (where $m∈Z$ and $h′(x)$ is the derivative of $h(x)$), find the maximum value of $m$.

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