
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
The rhombus $ABCD$ is divided into two equilateral triangles by its diagonal $BD$. Point $P$ is given on segment $AD$, and point $Q$ is given on segment $CD$ such that $\angle PBQ = 60^\circ$. What are the measures of the other two angles of triangle $PBQ$?

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