
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 the function $f(x) = ax^3 + bx^2 - 3x$ attains extreme values at $x = \pm 1$.
(1) Find the explicit formula for the function $f(x)$.
(2) If there are three tangent lines to the curve $y = f(x)$ passing through the point $A(1, m)$ (where $m \neq -2$), determine the range of the real number $m$.

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