
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
The sides opposite to the internal angles A, B, and C of $\triangle ABC$ are denoted as $a$, $b$, and $c$, respectively. It is given that $\sin(A+C) = 8\sin^2 \left(\frac{B}{2}\right)$.  
(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}
user