
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 that $O, A, B, C, E$ are points on a straight line with distances $OA = a$, $OB = b$, $OC = c$ and $OE = e$. Also, $P$ is a point on the line between $B$ and $C$ such that $AP:PD = 2 \cdot (BP:PC)$. Determine the coordinate $OP$.

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