
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 $XYZ$, $M$ lies on $\overline{YZ}$ extended past $Z$ such that $YM:MZ = 4:1$, and $N$ lies on $\overline{XZ}$ such that $XN:NZ = 3:2$. Let $Q$ be the intersection of lines $YN$ and $XM$.

Then
\[\overrightarrow{Q} = a \overrightarrow{X} + b \overrightarrow{Y} + c \overrightarrow{Z},\]where $a,$ $b,$ and $c$ are constants such that $a + b + c = 1.$  Enter the ordered triple $(a,b,c)$.

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