
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  $ABCD,$  leg  $\overline{BC}$  is perpendicular to bases  $\overline{AB}$  and  $\overline{CD},$  and diagonals  $\overline{AC}$  and  $\overline{BD}$  are perpendicular.  Given that  $AB=\sqrt{11}$  and  $AD=\sqrt{1001},$  find  $BC^2.$ 

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