
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 the coordinates of the three vertices of triangle $\triangle ABC$ as $A(2,1)$, $B(4,7)$, $C(-4,3)$, find:<br/>
$(1)$ Find the area of $\triangle ABC$;<br/>
$(2)$ Find the standard equation of the circumcircle of $\triangle ABC$.

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