
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
Suppose the graph of the function $f(x) = (4 - x^2)(ax^2 + bx + 5)$ is symmetric about the line $x = -\frac{3}{2}$. Find the maximum value of $f(x)$.

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