
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 the equation \(a \cos x + b \sin x + c = 0\) \((a^2 + b^2 \neq 0)\) has two distinct real roots \(\alpha\) and \(\beta\) in \([0, \pi]\), find the value of \(\sin (\alpha + \beta)\).

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