
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 a cube \(A B C D-A_{1} B_{1} C_{1} D_{1}\) with edge length 1, \(P, Q, R\) are the midpoints of edges \(A B, A D,\) and \(A A_1\) respectively. A right triangular prism is constructed with \(\triangle PQR\) as its base, such that the vertices of the other base also lie on the surface of the cube. Find the volume of this right triangular prism.

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