
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 line segment \(AB\), with \(P\) closer to \(A\) than \(Q\). \(P\) divides \(AB\) in the ratio \(3:4\) and \(Q\) divides \(AB\) in the ratio \(4:5\). If the length of segment \(PQ\) is 5 units, find the length of segment \(AB\).
A) \(150\)
B) \(105\)
C) \(315\)
D) \(240\)
E) \(280\)

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