"Look into" vs. "look at" in the 'investigate, explore' sense

Are look into and look at interchangeable? If not what are the differences between the two?

I will look at my options and see what I have.

I will look into my options and see what I have.

I will look into it and let you know. Or the government is going to look into the case.

Look at suggests that you already know what your options are and will review them, whereas look into suggests that you first need to investigate what those options might be.

In the above mentioned context,

Look into something: investigate, to inquire into

• Look into a question.
• The governor asked the police commissioner to look into the case.

Look at something: examine

• We must look at the question from all sides.
• Doctor, will you please look at my ankle?
• Will you please look at the battery of my car?

Usually, "look at" and "look into" are interchangeable. In such cases (of interchangeability) "look into something" suggests a more thorough examination (of something) than "look at something".

In the sentences you have provided, "look at" and "look into" can be interchanged.