
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
The sum of three numbers is 35. If the third number is increased by 1, they form an arithmetic sequence. If the first number is increased by 3, they form a geometric sequence. What are these three numbers?

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