
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
Let the positive integers $E, F, G$ form an arithmetic sequence and the integers $F, G, H$ form a geometric sequence. If $\frac{G}{F} = \frac{7}{4}$, what is the smallest possible value of $E + F + G + H$?

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