
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
Lines $p$ and $q$ are parallel. $m\angle X = 100^\circ$, and $m\angle Y = 130^\circ$. A third line $r$ intersects line $p$ at point $Z$. If $m\angle Z = 70^\circ$, what is the measure of $m\angle W$, the angle between line $r$ and line $q$ at their intersection point?

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