
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 $PQRS,$
\[\angle PSR = \angle PRQ = \angle QRS = 90^\circ.\]
Also, a = $\sin \angle PQS$ and b = $\sin \angle PRS$. Additionally, $PR = 2PQ$ and $\alpha = \cos \angle PSQ$. Express $\cos \angle PQR$ in terms of a, b, and $\alpha.$

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