
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 a quadratic function $f(x) = ax^2 + bx + c$ ($a, b, c \in \mathbb{R}$, and $a \neq 0$), when $x \in [-3, 1]$, we have $f(x) \leq 0$; when $x \in (-\infty, -3) \cup (1, +\infty)$, we have $f(x) > 0$, and $f(2) = 5$.  
(I) Find the expression of $f(x)$.  
(II) If the equation $f(x) = 9m + 3$ has real solutions for $x$, find the range of the real number $m$.

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