
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
The edge length of the cube \(A B C D - A_{1} B_{1} C_{1} D_{1}\) is 3. Points \(P, Q, R\) are located on edges \(A A_{1}, B B_{1}, C_{1} D_{1}\) respectively, with \(A_{1} P = 1\), \(B_{1} Q = 2\), \(C_{1} R = 1\). Let \(\alpha\) be the acute dihedral angle between plane \(P Q R\) and plane \(A B C D\). Find \(\alpha\).

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