
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 $f(x)=3(ax^{3}+bx^{2})$, with a maximum value of $3$ at $x=1$;  
$(Ⅰ)$ Find the values of $a$ and $b$;  
$(Ⅱ)$ Find the extreme values of the function $f(x)$ on the interval $\left[-1,3\right]$.

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