
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
Let \( x_{1} \) and \( x_{2} \) be the roots of the equation 
\[ 
x^{2} - 3 \sin \theta \cdot x + \sin^{2} \theta + 1 = 0 
\]
for \( x \in \mathbb{C} \) and \( \theta \in [0, \pi) \), and suppose that \( |x_{1}| + |x_{2}| = 2 \). Determine \( \theta \).

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