
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
The following diagram shows equilateral triangle  $\vartriangle ABC$  and three other triangles congruent to it. The other three triangles are obtained by sliding copies of  $\vartriangle  ABC$  a distance  $\frac18 AB$  along a side of  $\vartriangle ABC$  in the directions from  $A$  to  $B$ , from  $B$  to  $C$ , and from  $C$  to  $A$ . The shaded region inside all four of the triangles has area  $300$ . Find the area of  $\vartriangle ABC$ .
![Image](https://cdn.artofproblemsolving.com/attachments/3/a/8d724563c7411547d3161076015b247e882122.png)

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