
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
Let $P$ be the point on line segment $\overline{AB}$ such that $AP:PB = 4:1$. Then $\overrightarrow{P}$ can be expressed as $t \overrightarrow{A} + u \overrightarrow{B}$ for some constants $t$ and $u$. Find the ordered pair $(t,u)$.

[asy]
unitsize(1 cm);

pair A, B, P;

A = (0,0);
B = (5,0);
P = interp(A,B,4/5);

draw(A--B);

dot("$A$", A, W);
dot("$B$", B, E);
dot("$P$", P, N);
[/asy]

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