
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
A scientific calculator has a function key that raises the displayed number to the power of 3, and another key which replaces the displayed entry with its reciprocal. If one starts with a number $x \neq 0$, and uses the cube function followed by the reciprocal function repeatedly for $n$ cycles, what is the final result expressed as $y$?
A) $x^{3n}$
B) $x^{-3n}$
C) $x^{(-3)^n}$
D) $x^{3^n}$
E) $x^{(-1)^n3^n}$

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