
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]


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The positive integers \( A, B \) and \( C \) form an arithmetic sequence, while the integers \( B, C \) and \( D \) form a geometric sequence. If \( \frac{C}{B} = \frac{7}{4}, \) what is the smallest possible value of \( A + B + C + D \)?

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