
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
Six points $O, A, B, C, D, E$ lie in that order on a straight line with distances $OA=2a, OB=3a, OC=5a, OD=7a, OE=8a$. Point $P$ lies between points $B$ and $C$ such that the ratio $AP:PE = BP:PC$, and $P$ is located $\frac{2}{3}$ of the way from $B$ to $C$. Find the distance $OP$.
A) $4.33a$
B) $4.67a$
C) $5a$
D) $4a$
E) $4.5a$

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