
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 there is a calculator with a special key that replaces the number $x$ currently displayed with the number given by the formula $\frac{1}{1-x}$. Initially, the calculator displays the number 7. After the special key is pressed 101 times in a row, what number will the calculator display?

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