
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 the spatial quadrilateral $ABCD$, $E$, $F$, $G$, $H$ are the midpoints of $AC$, $BC$, $DB$, $DA$, respectively. If $AB=12\sqrt{2}$, $CD=4\sqrt{2}$, and the area of the quadrilateral $EFGH$ is $12\sqrt{3}$, then the angle formed by $AB$ and $CD$ is _______.

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