
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 \(O\) lie 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 \(H\) directly above \(O\). The balloon is held in place by four ropes \(HA\), \(HB\), \(HC\), and \(HD\). Rope \(HC\) has length 170 m and rope \(HD\) has length 140 m. Additionally, rope \(HA\) is given to be 150 m. How high is the balloon above the field (that is, the length of \(OH\))?

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