
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 $f(x)=x^{3}+3x^{2}-5 (x\in R)$ with its graph represented by the curve $C$.

1) Find the range of slopes of the tangent lines to the curve $C$ when $x\in [-2,1]$.
2) Find the equation of the line that is tangent to the curve $C$ and perpendicular to the line $l$: $\begin{cases} x= \frac {1}{2}+ \frac {3 \sqrt {10}}{10}t \\ y= \frac {1}{3}+ \frac { \sqrt {10}}{10}t\\ \end{cases}$ (where $t$ is a parameter).

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