
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 function $f(x)=e^{2x}+mx$, where $m\leqslant 0$.
- (I) When $m=-1$, find the equation of the tangent line to the curve $y=f(x)$ at the point $(0,f(0))$;
- (II) If the inequality $f(x) > 0$ always holds within its domain, find the range of the real number $m$.

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