
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
The parametric equations of a curve are given by $\begin{cases} x=1+2\cos \theta \\ y=2+3\sin \theta \end{cases}, (\theta \text{ is the parameter})$. Find the Cartesian equation of the curve.

A) $\dfrac {(x+1)^{2}}{4} - \dfrac {(y+2)^{2}}{9} = 1$
B) $\dfrac {(x-1)^{2}}{4} - \dfrac {(y-2)^{2}}{9} = 1$
C) $\dfrac {(x+1)^{2}}{4} + \dfrac {(y+2)^{2}}{9} = 1$
D) $\dfrac {(x-1)^{2}}{4} + \dfrac {(y-2)^{2}}{9} = 1$

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