
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
Four points $A$, $B$, $C$, $D$ in space satisfy $|\overrightarrow{AB}|=3$, $|\overrightarrow{BC}|=7$, $|\overrightarrow{CD}|=11$, and $|\overrightarrow{DA}|=9$. Determine the possible values of $\overrightarrow{AC} \cdot \overrightarrow{BD}$.

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