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The -mashō form and -ō|yō form are called the "volitional" forms
They are used to express intentions. Something like: "I will | I will have | Let's do something"
-mashō form I will | Let's ... (Formal) ___
-mashō form ka Shall I ... ? | Shall we (Formal) ___
-masen form ka Should I ... ? | Should we (Formal) ___
-ō|yō form Let's ... (Informal) ___
-ō|yō form + to kangaete imasu | iru [I think] I'll ... ___
-ō|yō form + to omou | omotte iru [I think] I'll ... ___