
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
It is known that the difference of the variable quantities \( z \) and \( y \) is proportional to the quantity \( x \), and the difference of the quantities \( x \) and \( z \) is proportional to the quantity \( y \). The proportionality coefficient is the same and is equal to a positive integer \( k \). A certain value of the quantity \( z \) is \( \frac{5}{3} \) times the difference of the corresponding values of \( x \) and \( y \). Find the numerical value of the coefficient \( k \).

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