
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
Five points \(O, A, B, C, D\) are positioned in order on a straight line with distances \(OA = 2a\), \(OB = b\), \(OC = 3c\), and \(OD = d\). Point \(E\) is also on the line such that \(OE = e\). Point \(P\) is a point on the line between \(B\) and \(C\) such that the ratio \(AP:PE = BP:PC\). Find the expression for \(OP\) in terms of \(a, b, c, d, e\).

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