
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
Find two numbers that can be inserted between $1$ and $16$ such that the sequence $1, a, b, 16$ forms a geometric progression with the first three terms and an arithmetic progression with the last three terms. What is the sum of those two numbers?
A) 12
B) 13
C) 14
D) 12.5
E) 12.64

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