
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 $Q$ lie on a line segment $AB$. Both points are on the same side of the midpoint of $AB$. Point $P$ divides $AB$ in the ratio $3:5$, and $Q$ divides $AB$ in the ratio $4:7$. If $PQ = 3$, then find the length of segment $AB$.
A) 280
B) 293
C) 294
D) 300
E) 315

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