
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
In acute triangle ABC, a, b, and c are the sides opposite to angles A, B, and C respectively, and $(a+c+b)(a+c-b)=(2+ \sqrt {3})ac$.

1. Find angle B.
2. If $\cos{A}+\sin{C}= \frac { \sqrt {6}}{2}$, $b= \sqrt {6}- \sqrt {2}$, find the area of triangle ABC.
3. Find the range of $\cos{A}+\sin{C}$.

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