
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
Let point $Q$ be in the plane $\alpha$ of triangle $ABC$, and point $P$ be outside the plane $\alpha$. If for any real numbers $x$ and $y$, $|\overrightarrow{AP} - x\overrightarrow{AB} - y\overrightarrow{AC}| \geq |\overrightarrow{PQ}|$, then the angle $\theta$ between vector $\overrightarrow{PQ}$ and vector $\overrightarrow{BC}$ is $\qquad$.

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