
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 $f(x)=x(2x^2-3x-12)+5$.
- $(1)$ Find the equation of the tangent line to the curve $y=f(x)$ at the point $x=1$.
- $(2)$ Find the maximum and minimum values of the function $y=f(x)$ in the interval $[0,3]$.

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