
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 a triangle \\(ABC\\) with its three internal angles \\(A\\), \\(B\\), \\(C\\) and the opposite sides \\(a\\), \\(b\\), \\(c\\) respectively, and the area \\(S\\), it satisfies \\(4S=a^{2}-(b-c)^{2}\\) and \\(b+c=8\\). The maximum value of \\(S\\) is \_\_\_\_\_\_.

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