There are a couple of ways to say this. Bragging is another word. If I were going to say this I would put it this way:
thanks to my — and I'm not boasting here — superior understanding and thinking skills.
Here, you can substitute bragging for boasting.
Of course, everyone knows that the writer is boasting, so this is probably intended to be humorous. Another way to say it:
thanks to my superior understanding and thinking skills (hey, if it's fact it ain't bragging).
Even though it's incorrect, ain't is used instead of isn't in this phrase (which is also intended to be humorous) to suggest the sort of uneducated wisdom that comes from common sense.