
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
Diameter $\overline{AB}$ of a circle with center $O$ is $16$ units. $C$ is a point $3$ units from $A$, and on $\overline{AB}$. $D$ is a point $5$ units from $B$, and on $\overline{AB}$. $Q$ is any point on the circle. Then the broken-line path from $C$ to $Q$ to $D$:
- Find the maximum possible length of this path.
A) $8$ units
B) $8\sqrt{3}$ units
C) $16$ units
D) $16\sqrt{3}$ units
E) $24$ units

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