
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
There are  $200$  numbers on a blackboard: $ 1! ,  2! ,  3! ,  4! , ... ... ,  199! ,  200!$ .
Julia erases one of the numbers. When Julia multiplies the remaining  $199$  numbers, the product is a perfect square. Which number was erased?

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