The problem is that $value$ does not return something like "1,7,30", instead, I could only get a single value, which is not enough for my further calculation. Any ways that I can get the full list of checked options? Thanks!
In this line <set token="query">(days=$value$)</set> try to replace $value$ with $field1$. The checkbox input token is field1 for your code as seen in this line :- <input type="checkbox" token="field1">.
Please see the code below where I was able to extract all the three values in a comma separated text and used it in the title of the panel and also in the text of the text box. Hope it helps.