
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 hyperbola $E$: $x^2-\frac{y^2}{b^2}=1(b>0)$, point $P(-2,-3)$ lies on $E$. <br/>$(1)$ Find the equation of $E$; <br/>$(2)$ A line $l$ passing through point $Q(0,-1)$ intersects $E$ at two distinct points $A$ and $B$ (both different from point $P$). Find the sum of the slopes of lines $PA$ and $PB$.

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