
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 the line segment \( \overline{AB} \) such that \( AP:PB = 4:1 \). Then the position vector \( \overrightarrow{P} \) can be expressed as a linear combination of \( \overrightarrow{A} \) and \( \overrightarrow{B} \) as \( \overrightarrow{P} = t \overrightarrow{A} + u \overrightarrow{B} \) for some constants \( t \) and \( u \). Find the ordered pair \( (t, u) \).

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