
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
The function $f(x) = 4x^3 + ax^2 + bx + 5$ is increasing on $(-\infty, -1)$ and $\left(\frac{3}{2}, +\infty\right)$, and it is decreasing on $(-1, \frac{3}{2})$.
1. Find the analytical expression for the function.
2. Calculate the maximum and minimum values of $f(x)$ on the interval $[-1, 2]$.

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