
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
A pool table is in the shape of a regular hexagon $ABCDEF$. A ball is struck from the midpoint $P$ of side $AB$, hits a point $Q$ on side $BC$, and then sequentially strikes the sides $CD$, $DE$, $EF$, $FA$, and finally hits a certain point on side $AB$. Given that $\angle BPQ = \theta$, find the range of values for $\theta$.

Hint: Use the principle that the angle of incidence is equal to the angle of reflection.

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