
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 real numbers \( x \), let
\[ f(x) = \frac{1}{\sqrt[2011]{1 - x^{2011}}}. \]
Evaluate \( (f(f(\ldots(f(2011)) \ldots)))^{2011} \), where \( f \) is applied 2010 times.

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