
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 $Q$ both lie on the line segment $AB$ and on the same side of its midpoint. $P$ divides $AB$ in the ratio $3:5$, and $Q$ divides $AB$ in the ratio $4:5$. If the distance $PQ$ is $3$ units, then the length of $AB$ is:
A) 42.2
B) 43.2
C) 44.2
D) 45.2

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