
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 $ABC,$ $D$ lies on $\overline{AB}$ such that $AD:DB = 3:2,$ and $G$ lies on $\overline{BC}$ such that $BG:GC = 1:3.$ Let $Q$ be the intersection of $\overline{AD}$ and $\overline{CG}.$ Find the point $\overrightarrow{Q}$ represented as $x \overrightarrow{A} + y \overrightarrow{B} + z \overrightarrow{C},$ where $x, y,$ and $z$ are constants satisfying $x + y + z = 1.$ Enter the ordered triple $(x, y, z).$

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