
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 $f(x) = x^2 - 4x + (2 - a)\ln x$, where $a \in \mathbb{R}$:
1. When $a = 8$, find:
   a. The interval where $f(x)$ is strictly increasing.
   b. The equation of the tangent line to the curve $y = f(x)$ at the point $(1, -3)$.
2. Find the minimum value of the function $f(x)$ on the interval $[e, e^2]$.

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