
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 placed on a plane. $A$ 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 now 180 m. A hot-air balloon is positioned directly above $O$ at point $H$. This balloon is held by four ropes: $HA$, $HB$, $HC$, and $HD$. The lengths of ropes $HC$ and $HD$ are now 170 m and 150 m, respectively. Calculate the height $OH$ of the balloon above the field.

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