
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
Call a positive real number ultra-special if it has a decimal representation that consists entirely of digits $0$ and $2$. For example, $2.020202\cdots$ and $20.002$ are ultra-special numbers. What is the smallest $n$ such that $2$ can be written as a sum of $n$ ultra-special numbers?
A) 14
B) 15
C) 16
D) 17
E) 18

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