
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 vectors $$\overrightarrow {m} = (a+c, b)$$, $$\overrightarrow {n} = (a-c, b-a)$$, and $$\overrightarrow {m} \perp \overrightarrow {n}$$, where A, B, C are the interior angles of triangle ABC, and a, b, c are the lengths of the sides opposite angles A, B, C respectively.  
(1) Find the size of angle C;  
(2) Find the range of values for $\sin A + \sin B$.

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