
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 $A=\{1, 2, 3, k\}$, $B=\{4, 7, a^4, a^2+3a\}$, where $a\in\mathbb{N}^*$, $x\in A$, $y\in B$, and $f: x\rightarrow y=3x+1$ is a function 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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