
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
Consider a cyclic parallelogram $ABCD$ inscribed in a circle where $AB = 6$ units and $AD = 5$ units. The diagonals $AC$ and $BD$ intersect at point $O$. Calculate the lengths $AO$ and $OC$.
A) $\sqrt{61}$
B) $\frac{\sqrt{61}}{2}$
C) $5$
D) $6$

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