
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
Find the explicit expression for the function $f(x)=4x^3+ax^2+bx+5$ whose tangent line at $x=1$ is $y=-12x$; 

(1) Determine the explicit form of $f(x)$;

(2) Find the maximum and minimum values of $f(x)$ on the interval $[-3,1]$.

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