
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
Suppose on a calculator with perfect accuracy, there is a key to cube (take the cube of a number) and another key to find the cubic reciprocal (take the reciprocal and then cube it) of a number. Starting with a non-zero number $x$, you perform the following two steps alternately: cube the number and then find its cubic reciprocal, $n$ times for each operation. What is the expression for the final result, $y$?
A) $x^{9^n}$
B) $x^{(-9)^n}$
C) $x^{(-9)^{3^n}}$
D) $x^{-27^n}$
E) $x^{(-27)^n}$

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