
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
The positive integers $X, Y$ and $Z$ form an arithmetic sequence, while the integers $Y, Z$ and $W$ form a geometric sequence. If $\frac{Z}{Y} = \frac{7}{4},$ what is the smallest possible value of $X + Y + Z + W$?

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