
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: $(\sqrt{2}-\sqrt{12}+\sqrt{\frac{1}{2}}) \cdot \sqrt{3}$.
2. Given that $2+\sqrt{3}$ is a root of the equation $x^2-4x+c=0$, find the other root of the equation and the value of $c$.

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