We thought he is planning to go on vacation after the first of the month.
I think thought is incorrect because the sequence of tense. Is my reason correct?
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The combination of "thought"—past tense—with "is planning"—present tense—is awkward. Typically you would use the same tense for both verbs. Either "We thought he was planning ..." or "We think he is planning ..."
Mixing tenses like this isn't necessarily wrong. If you said, "We think he was planning ..." you mean that in the present you are thinking this, but what you are thinking about is what he was planning to do in the past. Depending on context, this might mean that his plans have changed or may have changed.
"We thought he is planning ..." is awkward because you are saying that your thought was in the past but what you were thinking about is something in the present. How could you know yesterday what he did not plan until today? If you are trying to say that you were anticipating what he would plan, it is more common to use a conditional verb, like, "We thought he would plan to ...".
The sentence could be correct if your intent is to say that his plan is ongoing, and yesterday you thought it was one way but today you know that it is something else. Like, "Yesterday we thought he is planning to go to Denver, but today we know he is planning to go to Albany." In such a case the verb tenses would be arguably correct, but that's just not how people normally say it, so it sounds very strange.