
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
There are four numbers. The first three form an arithmetic sequence, and the last three form a geometric sequence. The sum of the first and the fourth numbers is 16, and the sum of the second and the third numbers is 12. Find these four numbers.

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