
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 selected on the graph of \(y = -x^2\) so that quadrilateral \(ABOC\) is square, where \(O\) is the origin and \(C\) is the point on the graph opposite to \(O\) along the diagonal line with \(A\) and \(B\). Find the length of the diagonal \(AC\) of the square.

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