
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
Consider a sequence of numbers defined recursively by \( s_1 = 2 \) and for \( n > 1 \) by \( s_n = 2 + s_{n/3} \) when \( n \) is divisible by 3, and by \( s_n = \frac{1}{s_{n-1}} \) when \( n \) is not divisible by 3. Given that \( s_n = \frac{23}{105} \), find \( n \).

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