
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
(1) Given the function $f(x) = \dfrac{1}{2}x^2 - (a+m)x + a\ln x$ and $f'(1) = 0$, where $a, m \in \mathbb{R}$, find the value of $m$;

(2) Given the function $f(x) = x^3 + 3x^2 - 9x - 3$, if the tangent line $l$ at the point $(x_0, f(x_0))$ on the graph of function $f(x)$ is perpendicular to the line $x - 9y + 1 = 0$, find the equation of the tangent line $l$.

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