
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
For a function $y=f(x)$ with domain $D$, if it satisfies the following conditions simultaneously:
1. $f(x)$ is either monotonically increasing or decreasing within $D$;
2. There exists an interval $[a,b] \subseteq D$ such that the range of $f(x)$ on $[a,b]$ is $[a,b]$; then we call $y=f(x) (x \in D)$ a closed function.
   1. Find the interval $[a,b]$ for the closed function $y=-x^{3}$ that meets condition 2.
   2. Determine whether the function $f(x)= \frac {x}{x+1}$ is a closed function, and explain the reason;
   3. If $y=k+ \sqrt {x+2}$ is a closed function, find the range of the real number $k$.

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