
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
An infinite sequence of decimal digits is obtained by writing the positive integers in order: 123456789101112131415161718192021 ... . Define f(n) = m if the 10^n th digit forms part of an m-digit number. For example, f(1) = 2, because the 10th digit is part of 10, and f(2) = 2, because the 100th digit is part of 55. Find f(1987).

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