
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
Given that in the rectangle \( UVWX \), \( UV = 20 \) and \( VW = 30 \), a vertical semi-circular wall with diameter \( XW \) is constructed, with point \( Z \) being the highest point on the wall, determine the perimeter of \( \triangle UVZ \).

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