
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 $XYZ,$ $W$ is a point on $\overline{YZ}$ extended past $Z$ such that $YW:WZ = 4:1,$ and $V$ is a point on $\overline{XZ}$ such that $XV:VZ = 2:3.$ Let $Q$ be the intersection of lines $YV$ and $XW.$ Determine the coefficients $(x, y, z)$ such that
\[\overrightarrow{Q} = x \overrightarrow{X} + y \overrightarrow{Y} + z \overrightarrow{Z}\]
where $x + y + z = 1.$

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