Omoimasu (Omou) is used when you are expressing that you are thinking of doing something. The usage is “Verb follow by Omoimasu”.

Example :
Q : What would you read? – Nani o yomimasu ka
A : I think I’m going to read a novel – Shōsetsu o (yomu)yomō to omoimasu

In the above example, the verb, “yomu (よむ)” is converted into “yomō (よもう）” which means “Let’s Read”. The converted verb “yomō” is same as the polite form-“yomimashō”. Example : Iku – Ikō ; Kaeru – Kaerō ; Nomu – Nomō. The conversion is simple, just change the last hiragana character to the 5th sound and add a “u” if you are writing in hiragana – よむ >> よもう. In romaji, the “mo u” is typed as “mō”.

When “to omoimasu” is used, you cannot use the polite form of verb follow by “to omoimasu”. For instance, “Yomimashō to omoimasu” is WRONG.

More examples :
Q : What would you listen? – Nani o kikimasu ka
A : I think I am going to listen to Japanese News – Nihongo no nyu-su o (kiku)kikō to omoimasu