
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
Consider a modified calculator that has a key for squaring the displayed number, and another key for taking the reciprocal. Now, let $z$ be the result after starting with a number $x \neq 0$, first taking its reciprocal, and then alternately squaring and taking reciprocals for a total of $n$ operations. What is the value of $z$?
A) $x^{2^n}$
B) $x^{-2^n}$
C) $x^{(-1)^{n+1} 2^n}$
D) $x^{(-1)^n 2^{\lfloor n/2 \rfloor}}$
E) $x^{(-1)^n n}$

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