
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
A sequence is defined as a "geometric sequence" if the product of every term and its subsequent term is a constant. This constant is referred to as the common ratio of the sequence. Given that $a_n$ is a geometric sequence with $a_1=2$ and a common ratio of $5$, derive the formula for the sum of the first $n$ terms, denoted as $S_n$:

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