
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 $ABC$, $a$, $b$, and $c$ represent the sides opposite to angles $A$, $B$, and $C$, respectively, with internal angles $A$, $B$, and $C$ satisfying $A+C=2B$. 

(1) If $b=2$, find the maximum value of the area of triangle $ABC$ and determine the shape of the triangle when the maximal area is achieved. 

(2) If $\frac{1}{\cos A} + \frac{1}{\cos C} = -\frac{\sqrt{2}}{\cos B}$, find the value of $\cos \frac{A-C}{2}$.

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