
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Given a mapping $f: A \to B$ from set A to set B, determine which of the following statements are correct:

1. Different elements in set A can have the same image in B.
2. A single element in set A can have different images in B.
3. There can be elements in set B that do not have a pre-image in A.

Present the answer in LaTex format: \boxed{Your answer}
user