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Reminds me of a Rush song.

Another good one :)

Believe / Think / and IMO are all synonyms for me.

I am not religious. They are just my current thoughts based upon the information I have. They are ever changing.

So when I say believe I am not speaking like a religious person and implying undoubting faith.

good man.
Unfortunately 'believe' has religious connotations for most people.
It's a hijacked word.
I try to use something else such as "I am convinced that..."
or something similar.