
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 quadrilateral $ABCD$, $O$ is the intersection point of diagonals $AC$ and $BD$. Given that $AC=4$, $\vec{BA} \cdot \vec{BC}=12$, $\vec{AO}= \vec{OC}$, $\vec{BO}=2 \vec{OD}$, then $\vec{DA} \cdot \vec{DC}=$ ______.

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