
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
When we learn about the translation of linear and quadratic function graphs, we know that by shifting the graph of the linear function $y=2x$ up by $1$ unit, we get the graph of $y=2x+1$; by shifting the graph of the quadratic function $y=x^{2}+1$ to the left by $2$ units, we get the graph of $y=(x+2)^{2}+1$. If we shift the graph of the inverse proportion function $y=\frac{6}{x}$ to the right by $3$ units, the corresponding function of the shifted graph is ______.

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