
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 tetrahedron \(PQRS\),
\[\angle PRS = \angle PQS = \angle QRS = 90^\circ.\] Also, let \(s = \sin \angle PQS\) and \(t = \sin \angle PRS\). Given that the length of \(RS\) is \(2k\) where \(k\) is a constant, express \(\cos \angle PQR\) in terms of \(s\), \(t\), and \(k\).

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