
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
 $2021$  copies of each of the number from  $1$  to  $5$  are initially written on the board.Every second Alice picks any two f these numbers, say  $a$  and  $b$  and writes  $\frac{ab}{c}$ .Where  $c$  is the length of the hypoteneus with sides  $a$  and  $b$ .Alice stops when only one number is left.If the minnimum number she could write was  $x$  and the maximum number she could write was  $y$  then find the greatest integer lesser than  $2021^2xy$ .

<details><summary>PS</summary>Does any body know how to use floors and ceiling function?cuz actuall formation used ceiling,but since Idk how to use ceiling I had to do it like this :(]</details>

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