
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
For a positive integer \( n \), we define the function \( P(n) \) to be the sum of the digits of \( n \) plus the number of digits of \( n \). For example, \( P(45) = 4 + 5 + 2 = 11 \).

(a) Determine \( P(2017) \).

(b) Determine all numbers \( n \) such that \( P(n) = 4 \).

(c) Determine with an explanation whether there exists a number \( n \) for which \( P(n) - P(n+1) > 50 \).

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