
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
(1) Calculate: $$\sqrt{3} + \sqrt{27} - \sqrt{12}$$  
(2) Calculate: $(\sqrt{3} + \sqrt{2})(\sqrt{3} - \sqrt{2}) - \frac{\sqrt{20} - \sqrt{15}}{\sqrt{5}}$  
(3) Solve the system of equations: $$\begin{cases} 2(x+1)-y=6 \\ x=y-1\end{cases}$$．

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