
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
Define the sequence $S_n$ as $S_n = \sum_{k=1}^{n} F_k$, where $F_k$ is the $k^{th}$ Fibonacci number, starting with $F_1 = 1$ and $F_2 = 1$. Find the first value of $n$ for which the units digit of $S_n$ is 5.

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