
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
Points \(A\) and \(B\) are chosen on the graph of \(y = -x^2\) so that triangle \(ABO\), with \(O\) as the origin, is isosceles right with \(OA = OB\). Determine the length of one side of triangle \(ABO\).

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