
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
A circle drawn through the vertices \( A \), \( B \), and \( D \) of a right trapezoid \( ABCD \) ( \(\angle A = \angle B = 90^\circ\) ) intersects the extension of the base \( BC \) and the extension of the lateral side \( CD \) at points \( M \) and \( N \) respectively, such that \( CM : CB = CN : CD = 1 : 2 \). Find the ratio of the diagonals \( BD \) and \( AC \) of the trapezoid.

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