
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 the parameter equation for curve C:
$$
\begin{cases}
x= \sqrt{t} - \frac {1}{\sqrt{t}} \\
y=3\left(t + \frac {1}{t}\right) + 2
\end{cases} \quad (t \ \text{is the parameter, } t > 0).
$$
Find the general equation of curve C.

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