
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
In the 46 right triangle \( ABC \), \(\angle A = 90^\circ\), there is an inscribed square \( PQRS \) with one side \( RS \) on the hypotenuse \( BC \), \( P \) on \( AB \), and \( Q \) on \( AC \). Given \( |AB| = a \) (\( a > 0, \ a \) is a constant), and \(\angle B = \theta\), when \(\theta\) changes, what is the minimum value of the ratio \( \frac{S_{\triangle ABC}}{S_{PQRS}} \)?

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