
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 triangle $\triangle ABC$, where $a$, $b$, and $c$ are the lengths of the sides opposite to angles $A$, $B$, and $C$ respectively. It is known that $\frac{2a+b}{c} = \frac{\cos(A+C)}{\cos C}$.

1. Find the measure of angle $C$.
2. Find the range of values for $\frac{a+b}{c}$.

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