Can you help me find a word?

I have been trying to remember a word for several days, and I feel like an idiot for not being able to.

What is the word to describe being careful with how much personal information one might reveal early on in a situation before knowing more facts?

Let me see if I can explain with an example. I knew a woman from a foreign country. She left and was replaced by another woman also from the same country. I was careful how I spoke about the first woman, until I knew whether the new woman had some kind of relationship with the first. What characteristic am I describing?

I feel like it starts with a “c”.

I’m completely blank and feeling silly.