
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 $f(x) = a(x - 5)^2 + 6\ln x$, where $a \in \mathbb{R}$, the tangent line to the curve $y = f(x)$ at the point $(1, f(1))$ intersects the $y$-axis at the point $(0, 6)$.

(1) Find the equation of the tangent line to the function $f(x)$ at the point $(1, f(1))$.

(2) Find the extreme values (maximum and minimum) of the function $f(x)$.

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