
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 $f(x)=kx+b$, whose graph intersects the $x$ and $y$ axes at points A and B respectively, with $\overrightarrow{AB}=2\overrightarrow{i}+2\overrightarrow{j}$ ($\overrightarrow{i}$, $\overrightarrow{j}$ are unit vectors in the positive direction of the $x$ and $y$ axes). The function $g(x)=x^{2}-x-6$ is also given.

1. Find the values of $k$ and $b$.
2. When $x$ satisfies $f(x) > g(x)$, find the minimum value of the function $\frac{g(x)+1}{f(x)}$.

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