
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
Let line segment $AB$ be divided by points $P$ and $Q$ such that $P$ divides $AB$ in the ratio $3:2$ (with $P$ closer to $A$) and $Q$ divides $AB$ in the ratio $2:3$. If the distance between $P$ and $Q$ is 5 units, find the length of $AB$.
A) 20
B) 22
C) 25
D) 30
E) 35

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