
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 trapezoid $ABCD$, $AB$ is parallel to $CD$, $AC$ is perpendicular to $BD$, and $A(1,7)$, $B(7,5)$, $C(4,1)$. Find:<br/>
$(1)$ The coordinates of point $D$;<br/>
$(2)$ The area of trapezoid $ABCD$.

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