
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
Let \\(\triangle ABC\\) have its internal angles \\(A, B, C\\) opposite to sides \\(a, b, c\\) respectively. Given that \\(b + a\cos C = 0\\) and \\(\sin A = 2\sin(A + C)\\).
\\((1)\\) Find the magnitude of angle \\(C\\).
\\((2)\\) Find the value of \\(\frac{c}{a}\\).

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