
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 $P$ lie on the circle shown and the measures of arcs $BQ$, $QD$, $AP$, and $PC$ are $42^\circ$, $38^\circ$, $20^\circ$, and $40^\circ$, respectively.  Find the sum of the measures of angles $X$ and $Q$, where $X$ is the angle ($\angle X$) subtended by arc $BP$ at the center of the circle.

[As the image can't be modified, assume new labels as per needed for understanding, but use the same image placeholder with Points $A$, $B$, $Q$, $D$, $C$, and $P$ labeled.]

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