
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 $AB \parallel CD$. Side $AD$ of trapezoid $ABCD$ is extended through $D$, and side $BC$ is extended through $C$, to meet at point $E$. Define $S$ as the degree-sum of angles $CDE$ and $DCE$, and $S'$ as the degree-sum of angles $BAD$ and $ABC$. If $r = S/S'$, determine $r$.

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