
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 points P and Q divide line segment AB such that P divides AB in the ratio 3:2 and Q divides AB in the ratio 4:5. If the distance between P and Q is 3, find the length of segment AB.
A) \(\frac{120}{7}\)
B) \(\frac{130}{7}\)
C) \(\frac{135}{7}\)
D) \(\frac{140}{7}\)
E) \(\frac{150}{7}\)

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