
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 $f(x)=mx^{3}-3(m+1)x^{2}+(3m+6)x+1$, where $m < 0$
1. If the monotonically increasing interval of $f(x)$ is $(0,1)$, find the value of $m$.
2. When $x\in[-1,1]$, the slope of any tangent line to the graph of $y=f(x)$ is always greater than $3m$. Find the range of $m$.

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