
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 sets $A=\{1, 2, 3, k\}$ and $B=\{4, 7, a^4, a^2 + 3a\}$, where $a \in \mathbb{N}^*$, $x \in A$, $y \in B$, and the function $f: x \mapsto y = 3x + 1$ maps elements from the domain $A$ to the codomain $B$, find the values of $a$ and $k$.

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