
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. Express the vector $\overrightarrow{P}$ in terms of the vectors $\overrightarrow{A}$ and $\overrightarrow{B}$, i.e., find constants $t$ and $u$ such that 
\[\overrightarrow{P} = t \overrightarrow{A} + u \overrightarrow{B}.\]

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