
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 hit from the midpoint \(P\) of \(AB\), strikes a point \(Q\) on the side \(BC\), and subsequently hits the sides \(CD\), \(DE\), \(EF\), and \(FA\) in sequence, finally landing on a certain point on the side \(AB\). Let \(\angle BPQ = \theta\). Find the range of \(\theta\). 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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