
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
Given in \\(\triangle ABC\\), \\(a^{2}+c^{2}=b^{2}+ \sqrt{2}ac\\).

\\((1)\\) Find the size of \\(\angle B\\);

\\((2)\\) Find the maximum value of \\(\sqrt{2} \cos A+\cos C\\).

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