
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 \( f(x)=x^{n}, x \in D, n \in \mathbf{N}^{*} \). Determine whether \( f(x)=x^{n} \) is a solution of the functional inequality
\[ f(x) + f(1-x) > 1 \]
If it is, find the domain \( D \); if not, provide an explanation.

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