
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 \( f(x) = \frac{1010x + 1009}{1009x + 1010} \), and define \( f^{(1)}(x) = f(x) \), \( f^{(i)}(x) = f(f^{(i-1)}(x)) \) for \( i = 2, 3, \cdots \). Determine \( f^{(n)}(x) \).

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