
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 segment $\overline{AB}$ is extended past $B$ to point $P$ such that the ratio $AP:PB$ is $7:2$. If
\[\overrightarrow{P} = t \overrightarrow{A} + u \overrightarrow{B},\]
determine the constants $t$ and $u$ to represent the position vector $\overrightarrow{P}$ in terms of $\overrightarrow{A}$ and $\overrightarrow{B}$.

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