
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 a regular tetrahedron $S-ABCD$ with a height of 2 and a side length of the base as $\sqrt{2}$, points $P$ and $Q$ are located on the segments $BD$ and $SC$ respectively. What is the shortest distance between $P$ and $Q$?

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