
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
Given a sequence $\{a_n\}$, if $a_1$, $a_2-a_1$, $a_3-a_2$, $\ldots$, $a_n-a_{n-1}$, $\ldots$, form a geometric sequence with the first term as 1 and a common ratio of $r$, determine the general formula for $a_n$.

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