We have reason to believe Faye manipulated the Ethics Board for person gain.

本句，不定式to believe Faye manipulated the Ethics Board for person gain 是reason 的定语。而不定式与reason 存在“动状关系”。即：

1. We have reason to believe Faye manipulated the Ethics Board for person gain.（原句）=

2. We have reason for which we believe Faye manipulated the Ethics Board for person gain.（变成定语从句）=

3. We have reason for to believe Faye manipulated the Ethics Board for person gain.

（简化定语从句为不定式）