
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 $Q$ such that $AQ:QB = 7:2$. Then,
\[\overrightarrow{Q} = x \overrightarrow{A} + y \overrightarrow{B}\]
for some constants $x$ and $y$. Determine the ordered pair $(x, y)$.

[asy]
unitsize(1 cm);

pair A, B, Q;

A = (0,0);
B = (5,1);
Q = interp(A,B,7/9);

draw(A--Q);

dot("$A$", A, S);
dot("$B$", B, N);
dot("$Q$", Q, N);
[/asy]

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