
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 vectors $\overrightarrow{a}=(a_n, 2)$, $\overrightarrow{b}=(a_{n+1}, \frac{2}{5})$, and $a_1=1$. If the sum of the first $n$ terms of the sequence $\{a_n\}$ is $S_n$, and $\overrightarrow{a} \parallel \overrightarrow{b}$, then calculate the value of $S_n$.

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