
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
If $\overrightarrow{OP}= \frac{3}{4} \overrightarrow{OA}+ \frac{1}{8} \overrightarrow{OB}+ \frac{1}{8} \overrightarrow{OC}$ for any point $O$ in space, determine the geometric relationship between the points $P, A, B, C$.

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