
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) Determine the number of digits in the product \(111111 \cdot 1111111111\), where the first factor has 6 digits and the second has 10 digits.

b) The numbers \(2^{2016}\) and \(5^{2016}\) are written side by side to form a single number \(N\) which has a number of digits that is the sum of the number of digits of the two numbers. For example, if we did this with \(2^{3}\) and \(5^{3}\), we would obtain the number 8125, which has 4 digits. Determine the number of digits of \(N\).

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