
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
$A$ and $B$ move uniformly along two straight paths intersecting at right angles at point $O$. When $A$ is at $O$, $B$ is $800$ yards short of $O$. In three minutes they are equidistant from $O$, and in $6$ more minutes they are again equidistant from $O$. Determine the ratio of $A$'s speed to $B$'s speed.
A) $3:4$
B) $4:5$
C) $5:6$
D) $2:3$
E) $1:2$

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