
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 $f(x)=e^{2x}$, $g(x)=kx+1$ where $k\in\mathbb{R}$.

(1) If the line $y=g(x)$ is tangent to the curve $y=f(x)$, find the value of $k$.

(2) When $k > 0$, if there exists a positive real number $m$, such that for any $x\in(0,m)$, $|f(x)-g(x)| > 2x$ always holds, find the range of values for $k$.

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