
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 the sequence of numbers defined recursively by $t_1=2$ and for $n>1$ by $t_n=2+t_{n/3}$ when $n$ is divisible by 3, and by $t_n=\frac{1}{t_{n-1}}$ when $n$ is not divisible by 3. Given that $t_n=\frac{3}{29}$, find $n$.

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