
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 that \( a \) and \( b \) are integers, and the equation \( x^{2} + a x + 2 b^{2} = 0 \) has two roots \( \sin \alpha \) and \( \cos \alpha \) where \( 0 \leqslant \alpha < 2 \pi \), then what are all possible values of \( a + b \)?

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