
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 \(AB=3\) and \(AD=\sqrt{3241}\), find \(BC^2\).

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