
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 that $f(x)$ is a quadratic function, the solution set of the inequality $f(x) < 0$ is $(0, 5)$, and the maximum value of $f(x)$ on the interval $[-1, 4]$ is $12$.
(I) Find the analytical expression of $f(x)$;
(II) Solve the inequality $\frac{2x^2 + (a - 10)x + 5}{f(x)} > 1$ with respect to $x$ ($a < 0$).

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