
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 convex quadrilateral  $KLMN$  side  $\overline{MN}$  is perpendicular to diagonal  $\overline{KM}$ , side  $\overline{KL}$  is perpendicular to diagonal  $\overline{LN}$ ,  $MN = 65$ , and  $KL = 28$ . The line through  $L$  perpendicular to side  $\overline{KN}$  intersects diagonal  $\overline{KM}$  at  $O$  with  $KO = 8$ . Find  $MO$ .

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