1humble (kenjōgo) form of 'to know' or 'to be aware of' (used to express one's awareness modestly)
その件については存ずるところがございますが、詳しくは後ほど報告します。
I am aware of that matter, but I will report the details later.
お名前は存じておりますが、面識はございません。
I know your name, but I have not had the pleasure of meeting you.
そう存ずる次第でございます。
That is what I believe/think (humble, formal).
2humble form of 'to think' or 'to consider'; used to modestly express one's opinion or judgment
私はその案は実行可能だと存ずる。
I believe that proposal is feasible (humble).
今回の件は慎重に対応すべきだと存ずる次第です。
I am of the opinion that this matter should be handled carefully (humble/formal).