
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 that the graph of the function $y=a^{x-2}+1$ (where $a>0$ and $a \neq 1$) passes through the fixed point $P(m, n)$, and the line $l$ passing through point $Q(m-1, n)$ is intersected by the circle $C: x^2+y^2+2x-2y-7=0$ with a chord length of $3\sqrt{2}$, then the slope of line $l$ is \_\_\_\_\_\_.

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