
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 $2$ and $12$ in such a way that the sequence of the first three numbers form a geometric progression and the sequence of the last three numbers form an arithmetic progression. Find the sum of these two numbers.
A) 10
B) 11
C) 12
D) 13

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