
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
Four points $A$, $B$, $C$, $D$, and a center point $O$ are on a field. $A$ is north of $O$, $B$ is west of $O$, $C$ is south of $O$, and $D$ is east of $O$. The distance between $A$ and $B$ is 100 m. A kite is flying at point $K$ directly above $O$. The kite is tethered by ropes $KA$, $KB$, $KC$, and $KD$. Rope $KA$ is 120 m long and rope $KB$ is 110 m. Determine the height of the kite above the field (length of $OK$).

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