
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 $A$, $B$, $Q$, $D$, $C$, and $E$ lie on a circle. The measures of arcs $BQ$, $QD$, and $DE$ are $60^\circ$, $40^\circ$, and $50^\circ$, respectively. Calculate the sum of the measures of angles $P$ and $Q$, where $P$ is the angle at point $B$ formed by lines $BA$ and $BE$, and $Q$ is the angle at point $D$ formed by lines $DC$ and $DE$.

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