
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 four numbers where the first three form a geometric progression and the last three form an arithmetic progression. The sum of the first and last numbers is 21, and the sum of the middle two numbers is 18.

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