
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 function $f(x) = ax^3 + bx^2 - 3x$ $(a, b \in \mathbb{R})$, the equation of the tangent line at point $(1, f(1))$ is $y + 2 = 0$.  
(1) Find the analytical expression of the function $f(x)$;  
(2) If for any two values of the independent variable $x_1$ and $x_2$ in the interval $[-2, 2]$, it holds that $|f(x_1) - f(x_2)| \leq c$, find the minimum value of the real number $c$;  
(3) If it is possible to draw three tangent lines to the curve $y = f(x)$ passing through point $M(2, m)$ $(m \neq 2)$, determine the range of values for the real number $m$.

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