
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
Let  $ABCD$  be a quadrilateral with an inscribed circle, centre  $O$ . Let 
\[AO = 5, BO =6, CO = 7, DO = 8.\] 
If  $M$  and  $N$  are the midpoints of the diagonals  $AC$  and  $BD$ , determine  $\frac{OM}{ON}$  .

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