
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 the sides \\(a\\), \\(b\\), and \\(c\\) opposite the angles \\(A\\), \\(B\\), and \\(C\\) of \\(\triangle ABC\\), respectively, and that \\(b^{2}=3ac\\):
\\((I)\\) If \\(a=b\\), find \\(\cos B\\);
\\((II)\\) Let \\(B=120^{\circ}\\) and \\(a= \sqrt{2}\\), find the area of \\(\triangle ABC\\).

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