
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
Insert two positive numbers between $5$ and $12$ so that the sequence $5, x, y$ forms a geometric progression and $x, y, 12$ forms an arithmetic progression. Find the sum of $x$ and $y$.
A) 15.25
B) 16.25
C) 16.2788
D) 17.25

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