
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
Given that the radius of circle $C$ is $3$, and a point $D$ on the diameter $AB$ satisfies $\overrightarrow{AB} = 3\overrightarrow{AD}$, $E$ and $F$ are the endpoints of another diameter. Calculate the dot product of vectors $\overrightarrow{DE}$ and $\overrightarrow{DF}$.

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