
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 \(ABCD\) be a right trapezoid with bases \(AB\) and \(CD\), featuring right angles at \(A\) and \(D\). Given that the shorter diagonal \(BD\) is perpendicular to the side \(BC\), determine the minimum possible value for the ratio \(\frac{CD}{AD}\).

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