
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 billiard table is in the shape of a regular hexagon $A B C D E F$. A ball is struck from the midpoint $P$ of side $A B$, hits a point $Q$ on side $B C$, and then successively hits the sides $C D$, $D E$, $E F$, and $F A$, finally hitting a point on side $A B$. Given that $\angle B P Q = \theta$, determine the range of possible values for $\theta$.

Hint: Use the principle that the angle of incidence equals the angle of reflection.

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