
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 the line segment $AB$ such that $P$ divides $AB$ in the ratio $3:2$ and $Q$ divides $AB$ in the ratio $5:3$. Given that the distance between $P$ and $Q$ is $3$ units, find the length of segment $AB$.
A) 100  
B) 110  
C) 120  
D) 130

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