
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 \( a \) be a given real number, \( n \) be a natural number, \( n > 1 \).

Find all \( x \) such that the sum of the \( n \)-th roots of the numbers \( x^{n} - a^{n} \) and \( 2 a^{n} - x^{n} \) equals \( a \).

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