
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 $f(x) = x^3 + ax^2 + bx + c$ whose graph passes through the origin, and $f(x)$ has extreme values at $x = -1$ and $x = 3$.

(1) Find the intervals of monotonicity and the extreme values of the function $f(x)$;  
(2) If the graph of the function $y = f(x)$ has exactly one common point with the graph of $y = m$, find the range of values for the real number $m$.

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