
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 triangle \(ABC\), the sides opposite to angles \(A\), \(B\), and \(C\) are denoted by \(a\), \(b\), and \(c\) respectively. It is known that \(\sin(A + C) = 8\sin^2\frac{B}{2}\).
1. Find \(\cos B\);
2. If \(a + c = 6\) and the area of \(\triangle ABC\) is 2, find \(b\).

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