
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
A circle with center $O$ has a radius of $9$. Triangle $DEF$ is equilateral with $\overline{EF}$ as a chord of the circle, where $O$ is outside $\triangle DEF$ and $OD = 6$. Find the side length of $\triangle DEF$.

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