
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 $Q$ be a point on line segment $\overline{CD}$ such that $CQ:QD = 4:1$ and the magnitude of $\overrightarrow{D}$ is twice the magnitude of $\overrightarrow{C}$. Then express $\overrightarrow{Q}$ as a linear combination of $\overrightarrow{C}$ and $\overrightarrow{D}$ using constants $m$ and $n$. Enter the ordered pair $(m,n)$.

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