
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 $P$, $Q$, $R$, $S$, and $T$ lie on a plane. $P$ is directly north of $T$, $Q$ is directly west of $T$, $R$ is directly south of $T$, and $S$ is directly east of $T$. The distance between $R$ and $S$ is 160 m. A drone is flying directly above $T$ at point $U$. The drone is connected by four wires: $UP$, $UQ$, $UR$, and $US$. Wire $UR$ has a length of 170 m and wire $US$ has a length of 150 m. Determine the height of the drone above the plane (i.e., the length of $TU$).

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