
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 triangle \\(\Delta ABC\\), the lengths of the sides opposite to angles \\(A, B, C\\) are \\(a, b, c\\) respectively. It is known that \\((a+b+c)(b+c-a)=3bc,\\) and \\(\vec{AB} \cdot \vec{CA} = -1\\).

   \\((1)\\) Find the value of angle \\(A\\);

   \\((2)\\) If \\(b-c=1\\), find the value of \\(a\\).

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