
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 \( \triangle ABC \) with interior angles \( A, B, C \) and opposite sides \( a, b, c \) respectively, consider the vectors \( \boldsymbol{m} = (\sin A, b+c) \) and \( \boldsymbol{n} = (\sin C - \sin B, a - b) \). Suppose there exists a real number \( \lambda \) such that \( \boldsymbol{m} = \lambda \boldsymbol{n} \).
(1) Find the measure of angle \( C \);
(2) If \( a + b = kc \), find the range of the real number \( k \).

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