
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 $f(x) = \frac{ax^2}{x + b}$ (where $a$, $b$ are constants), the equation $f(x) = 2x + 3$ has two real roots: -2 and 3.
1. Find the minimum value of the function $f(x)$ when $x>2$.
2. Solve the inequality $f(x) < \frac{k(x-1) + 1 - x^2}{2-x}$, where $k$ is a parameter.

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