
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 $f(x) = -x^3 + ax^2 + b$ ($a, b \in \mathbb{R}$).
1. Let the function $g(x) = f(x) - b$. If $a = 1$, find the equation of the tangent line to the function $g(x)$ at the point $(1, g(1))$.
2. If the function $f(x)$ is increasing on the interval $(0, 2)$, find the range of values for $a$.

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