
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
a) Find the sum of the series 1 + 11 + 111 + ... + 111...1, where the last number contains $\mathbf{n}$ ones.
b) Find the sum of a similar series, but with fives instead of ones.

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