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I do not think "Illustrating" is used as a gerund here.
It sounds more like a verb.

Edit: A gerund is a verbal noun.
If it was used as a noun, then it would be a gerund.
He likes illustrating...

There is nothing wrong with

"President Putin recently said..."

It sounds strange. I cannot say whether or not it is gramatically correct
since I am not an English teacher.

Here is my best guess at what you are trying to say.

President Putin recently...