
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 all non-negative real values of the variable \( x \), the function \( f(x) \) satisfies the condition \( f(x+1) + 1 = f(x) + \frac{43}{(x+1)(x+2)} \). Calculate \( \frac{101}{f(2020)} \), given that \( f(0) = 2020 \).

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