
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
Let the function $f(x)= \frac {ax-1}{x+1}$, where $a\in\mathbb{R}$.  
$(1)$ If $a=1$, the domain of $f(x)$ is the interval $[0,3]$, find the maximum and minimum values of $f(x)$;  
$(2)$ If the domain of $f(x)$ is the interval $(0,+\infty)$, find the range of $a$ such that $f(x)$ is a monotonically decreasing function within its domain.

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