
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
Given that the height of a regular quadrangular pyramid \( S-ABCD \) is 2, and the side length of the base is \( \sqrt{2} \), points \( P \) and \( Q \) are located on segments \( BD \) and \( SC \) respectively, find the shortest distance between points \( P \) and \( Q \).

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