Loop through all database and do something

I code this :

declare @database varchar(50)
declare @strSwitchDB nvarchar(100)
declare @count int
declare @maxRow int
SET @count = 1
SELECT @maxRow=max(database_id) FROM sys.databases
WHILE (@count <= @maxRow)
BEGIN
SELECT @database = name FROM sys.databases WHERE database_id = @count
set @strSwitchDB='use '+@database
print 'do something here, processing'
EXEC sp_executesql @strSwitchDB
set @count=@count+1
END

I expected the process will run in all databases in SQL server
example :
use master
do something
use tempdb
do something
use msdb
do something


but it actually no return expected result. The process will run in same database instead run in all database.

example
use master
do something
do something
do something

I actually find another way to do this
if we want to loop through all database and do something,
we actually can write in one line

EXECUTE sp_msforeachdb 'SELECT ''[?]'', count(1) from [?].dbo.sysobjects'

Result
It actually loop through all the database and count number of row in sysobjects table
-------- -----------
[master] 3594
-------- -----------
[tempdb] 67
------- -----------
[model] 47
------ -----------
[msdb] 754

JFYI,The above is for example and not the the actually action I want to perform