
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 acute \\(\triangle ABC\\), \\(a\\), \\(b\\), and \\(c\\) are the sides opposite to angles \\(A\\), \\(B\\), and \\(C\\) respectively. The area of \\(\triangle ABC\\) is \\(S=2\\), and it satisfies \\(a\cos B=b(1+\cos A)\\). The range of \\((c+a-b)(c+b-a)\\) is \_\_\_\_\_\_.

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