What is the remainder when $7!$ is divided by $23$?

(Note: $n!$ means "n factorial", defined as the product of all integers from $1$ to $n$.)
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
What is the remainder when $7!$ is divided by $23$?

(Note: $n!$ means "n factorial", defined as the product of all integers from $1$ to $n$.)
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
3
What is the remainder when $7!$ is divided by $23$?

(Note: $n!$ means "n factorial", defined as the product of all integers from $1$ to $n$.)
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