
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 point $O$ is the origin of coordinates, point $A$ in the first quadrant lies on the graph of the inverse proportional function $y=\frac{1}{x}$ for $x>0$, and point $B$ in the second quadrant lies on the graph of the inverse proportional function $y=-\frac{4}{x}$ for $x<0$, and $O A$ is perpendicular to $O B$, find the value of $\tan \angle A B O$.

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