
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
Let  $k{}$  be a positive integer. For every positive integer  $n \leq 3^k$ , denote  $b_n$  the greatest power of  $3$  that divides  $C_{3^k}^n$ . Compute  $\sum_{n=1}^{3^k-1} \frac{1}{b_n}$ .

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