
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 the function $f(x) = x^3 - 3x^2 - 9x$, $g(x) = 15x + a$.

(1) Find the extreme values of $f(x)$;  
(2) If the graph of $f(x)$ intersects with the graph of $g(x)$ at exactly three points, find the range of values for $a$.

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