
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 starting with one, where each subsequent term is equal to double the sum of all previous terms. Find the smallest number such that the term at this position is divisible by $3^{2017}$.

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