
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
In triangle $XYZ,$ point $D$ is on $\overline{YZ}$ extended past $Z$ such that $YD:DZ = 4:1,$ and point $E$ is on $\overline{XZ}$ such that $XE:EZ = 3:2.$ Let \( F \) be on \( \overline{XY} \) such that \( XF:FY = 2:1 \). Let $P$ be the intersection of lines $BF$ and $YD.$ Determine the coordinates of $P$ in terms of $X$, $Y$, and $Z$.

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