
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 trapezoid with  $AB\parallel DC$ . Let  $M$  be the midpoint of  $CD$ . If  $AD\perp CD, AC\perp BM,$  and  $BC\perp BD$ , find  $\frac{AB}{CD}$ .

[i]Proposed by Nathan Ramesh

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