
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
Which quadratic equation has roots that are the squares of the roots of the equation

$$
\sin 2 \alpha \cdot x^{2} - 2(\sin \alpha + \cos \alpha) x + 2 = 0
$$

Solve the obtained equation.

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