
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 $\triangle ABC$, if $\sin A + \sin B = \sin C (\cos A + \cos B)$.
(1) Determine the shape of $\triangle ABC$;
(2) In the above $\triangle ABC$, if the side opposite to angle $C$ is $c=1$, find the range of values for the inradius of the triangle.

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