
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
Let $f(x) = ax^2 + bx + c$, where $a \neq 0$.  
(I) $f(x) = x$ has two real roots $x_1, x_2$, with $0 < x_1 < x_2 < \frac{1}{a}$. For $x \in (0, x_1)$, compare the magnitude of $f(x)$ and $x_1$.  
(II) If the solution set for $|f(x)| < 1$ is $(-1, 3)$, determine the range of $a$.

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