
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 $\{a_n\}$ be the sequence formed by arranging all the numbers in the set $\{3^p+3^q+3^r|0\leq p<q<r, \text{ and } p, q, r \in \mathbb{N}^*\}$ in ascending order. Given that $a_k = 2511$, find $k$.

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