
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 flat 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 160 m. A hot-air balloon is positioned in the air at point $H$ directly above $O$. This balloon is held in place by ropes $HA$, $HB$, $HC$, and $HD$. The length of rope $HC$ is 170 m and the length of rope $HD$ is 150 m. Determine the height of the balloon above the field, that is, the length of $OH$.

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