The word “over-rely” does not seem to appear in online dictionaries, so I’m not sure if I can use it safely. Is there a good synonym?
Here’s an example:
Don’t over-rely on Google for searching the Web.
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It's perfectly fine to use "over-rely", and it does appear in dictionaries. The word rely is the verb form of the noun reliance.
Excessive dependence on or trust in someone or something:
an over-reliance on technology
Abuse: : to use excessively ('abuse alcohol'); to use without medical justification ('abusing painkillers'); to use wrongly, misuse ('abuse privileges'); to use improperly or in harmful amounts ('abuse drugs').
In many contexts an over-reliance on something implies misuse of that thing, such as a drug. In the case of your Google search example (as in "Don't abuse Google for searching the web") the meaning of 'Abuse' may not be entirely clear, as searching the web is the proper purpose for which Google was made. You could rephrase the sentence to something more specific to your situation (e.g. "Don't abuse Google for conducting a literature review") that conveys a meaning of both misuse and 'over-reliance'.