
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 that $y=f(x)$, $x\in D$ (where $D$ is the domain of the function), satisfies the following two conditions:
1. The function $f(x)$ is either monotonically increasing or monotonically decreasing on $D$;
2. There exists an interval $[a,b]\subseteq D$ such that the range of $f(x)$ on $[a,b]$ is $[a,b]$. Then $y=f(x)$, $x\in D$ is called a closed function. Answer the following questions:
1. Determine whether the function $f(x)=3^{x}$ ($x\in (0,+\infty)$) is a closed function and explain your reasoning.
2. If $y=k+\sqrt{x}$ ($k<0$) is a closed function, find the range of $k$.

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