
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 unit vectors $\overrightarrow {e_{1}}$ and $\overrightarrow {e_{2}}$ are parallel to the positive directions of the $x$-axis and $y$-axis, respectively, and the vectors $\overrightarrow {AC}=3\overrightarrow {e_{1}}-\overrightarrow {e_{2}}$ and $\overrightarrow {BD}=2\overrightarrow {e_{1}}+6\overrightarrow {e_{2}}$, calculate the area of the quadrilateral $ABCD$.

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