
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
The equation \(2008=1111+444+222+99+77+55\) is an example of decomposing the number 2008 as a sum of distinct numbers with more than one digit, where each number's representation (in the decimal system) uses only one digit.

i) Find a similar decomposition for the number 2009.

ii) Determine all possible such decompositions of the number 2009 that use the minimum number of terms (the order of terms does not matter).

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