
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
On the graph of the curve $y=x^2+1$, take a point $(1,2)$ and a nearby point $(1+\Delta x, 2+\Delta y)$. Then, the limit of $\frac{\Delta y}{\Delta x}$ as $\Delta x$ approaches 0 is \_\_\_\_\_.

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