
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
Given points O, A, B, C, D are taken in order on a straight line with distances OA = a, OB = b, OC = c, OD = d, and point Q is on this line such that OQ = q. Point P is on the line between B and C such that AP : PD = BP : PC and P is twice as far from O as Q is. Determine the length of OP.

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