
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 $f(x)=x^{3}+mx^{2}+nx$ $(m,n\in\mathbb{R})$.
- (I) If $f(x)$ has a maximum value at $x=1$, find the range of real numbers $m$.
- (II) If $f′(1)=0$, and there are exactly two tangents passing through the point $P(0,1)$ that are tangent to the curve $y=f(x)$, find the value of the real number $m$.

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