
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 a convex quadrilateral \(ABCD\), the diagonals \(AC\) and \(DB\) are perpendicular to sides \(DC\) and \(AB\) respectively. From point \(B\), a perpendicular is dropped to side \(AD\), intersecting \(AC\) at point \(O\). Find \(AO\) if \(AB = 4\) and \(OC = 6\).

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