
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 $O$ are located on a flat plane where $A$ 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 160 m. A kite is flying directly above point $O$ at point $K$. The kite is tethered by strings $KA$, $KB$, $KC$, and $KD$. The lengths of strings $KA$ and $KB$ are 170 m and 140 m, respectively. Find the altitude of the kite above the plane (i.e., the length of $OK$).

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