
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 three types of regular polygons with equal side lengths, used to tile a floor such that their vertices coincide and fit perfectly without gaps, and the number of sides of these three types of regular polygons are \( x \), \( y \), and \( z \) respectively, calculate the value of \( \frac{1}{x} + \frac{1}{y} + \frac{1}{z} \).

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