
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
Three numbers that sum to 114 are consecutive terms of a geometric sequence with a common ratio not equal to 1. They are also the 1st term, 4th term, and 25th term of an arithmetic sequence. Find these three numbers.

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