
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
Five points $A$, $B$, $C$, $D$, and $O$ are positioned on a field. $A$ is directly north of $O$, $B$ is directly west of $O$, $C$ is directly south of $O$, and $D$ is directly east of $O$. The distance between $C$ and $D$ is increased to 160 m. A kite is held in the air at point $K$ directly above $O$ and is tied with four strings: $KA$, $KB$, $KC$, and $KD$ where string $KC$ has a length of 170 m and string $KD$ has a length of 150 m. Find the height of the kite above the field, that is, the length of $OK$.

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