
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 \\(\Delta ABC\\), \\(a\\), \\(b\\), and \\(c\\) are the sides opposite to angles \\(A\\), \\(B\\), and \\(C\\) respectively, and it is given that \\(2a\sin A=(2b+c)\sin B+(2c+b)\sin C\\).

\\((1)\\) Find the magnitude of \\(A\\).

\\((2)\\) If \\(a=4\\), find the maximum value of \\(b+c\\).

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