
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
Points $P$ and $Q$ are on line segment $AB$, and both points are on the same side of the midpoint of $AB$. Point $P$ divides $AB$ in the ratio $3:4$, and $Q$ divides $AB in the ratio $4:5$. If the distance between points $P$ and $Q$ is 3 units, what is the length of segment $AB$?
A) 150
B) 168
C) 175
D) 189
E) 210

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