
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 defined recursively as follows: \( t_{1} = 1 \), and for \( n > 1 \):

- If \( n \) is even, \( t_{n} = 1 + t_{\frac{n}{2}} \).
- If \( n \) is odd, \( t_{n} = \frac{1}{t_{n-1}} \).

Given that \( t_{n} = \frac{19}{87} \), find the sum of the digits of \( n \).

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