
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 $f(x)=2ax- \frac {3}{2}x^{2}-3\ln x$, where $a\in\mathbb{R}$ is a constant,  
$(1)$ If $f(x)$ is a decreasing function on $x\in[1,+\infty)$, find the range of the real number $a$;  
$(2)$ If $x=3$ is an extremum point of $f(x)$, find the maximum value of $f(x)$ on $x\in[1,a]$.

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