
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
Line segments $\overline{AB}$ and $\overline{BC}$ are such that $B$ is between $A$ and $C$. $\overline{BC}$ is extended past $C$ to a point $P$ such that $BP:PC = 7:3$. Then
\[
\overrightarrow{P} = x \overrightarrow{B} + y \overrightarrow{C}
\]
for some constants $x$ and $y$. Find the ordered pair $(x,y)$.

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