
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
Line segment \( PQ \) has endpoints at \( P(6,-2) \) and \( Q(-3,10) \). Point \( R(a, b) \) is a point on \( PQ \) such that the distance from \( P \) to \( R \) is one-third the distance from \( P \) to \( Q \). What is \( b-a \) ?

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