
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 $ABC$, where the sides opposite angles $\angle A$, $\angle B$, and $\angle C$ are $a$, $b$, and $c$, respectively. There is an equation $a(1-x^2) + 2bx + c(1+x^2) = 0$ that has two equal real roots. It's also given that $3c = a + 3b$.  
(1) Determine the shape of $\triangle ABC$;  
(2) Find the value of $\sin A + \sin B$.

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