
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 set $A = \{x | x = n^2, n \in \mathbb{Z}\}$ and the function $f: A \rightarrow B$ defined by $f(x)$ as the remainder when $x$ is divided by $5$, calculate the number of elements in $B$ such that for all $y \in B$, there exists an $x \in A$ such that $f(x) = y$.

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