
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 the following correspondences between two sets:
(1) A={students in your class}, B={weights}, mapping f: each student corresponds to their own weight;
(2) M={1,2,3,4}, N={2,4,6,8}, mapping f: $n=2m$;
(3) X=$\mathbb{R}$, Y={non-negative real numbers}, mapping f: $y=x^3$.
Indicate how many of these are mappings and how many of these are functions.

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