
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 $f(x) = x^3 - 3ax - 1$ has an extremum at $x = -1$.

(1) Find the value of $a$, and determine the range of $f(x)$ on the interval $[-2, 3]$.

(2) If the line $y = 9x + m$ has three distinct common points with the graph of $y = f(x)$, find the range of $m$.

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