
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 points $P$ and $Q$ such that $AP:PB = 7:2$ and $AQ:QB = 5:1$ respectively. Express $\overrightarrow{P}$ and $\overrightarrow{Q}$ in terms of $\overrightarrow{A}$ and $\overrightarrow{B}$ and find the ordered pairs $(t_P, u_P)$ and $(t_Q, u_Q)$ for $\overrightarrow{P}$ and $\overrightarrow{Q}$, respectively.

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