
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 $f(x)=\frac{ax}{x^2+b}$, and the graph of $f(x)$ is tangent to the line $y=2$ at $x=1$.
1. Find the explicit formula of the function $f(x)$.
2. If $P(x_0, y_0)$ is any point on the graph of $f(x)$ and line $l$ is tangent to the graph of $f(x)$ at point $P$, find the range of possible slopes $k$ for line $l$.

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