
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
Triangles \( ABC \) and \( ADE \) have areas 4000 and 12000, respectively, with \( B=(0,0) \), \( C=(400,0) \), \( D=(1000,500) \), and \( E=(1010,515) \). What is the sum of all possible \( x \)-coordinates of \( A \)?

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