
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
Let \(f_{0}(x)=\frac{1}{c-x}\) and \(f_{n}(x)=f_{0}\left(f_{n-1}(x)\right)\), \(n=1,2,3, \ldots\). If \(f_{2000}(2000)=d\), find the value of \(d\).

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