
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
Points $A$, $B$, $C$, $D$, and $E$ lie on a circle. The measures of arcs $AB$ and $BC$ are $50^\circ$ and $60^\circ$, respectively. Find the sum of the measures of angles $R$ and $S$, where points $R$ and $S$ are defined by the intersections of lines $AD$ and $BE$, and $AC$ and $BD$, respectively.

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