
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 cube \( ABCD-A'B'C'D' \) with edge length 1, a point \( P \) is taken on the edge \( AC \). A plane is formed through points \( P, A', B' \), intersecting the base, which makes a dihedral angle \( \alpha \). Another plane is formed through points \( P, B', C' \), intersecting the base, which makes a dihedral angle \( \beta \). Find the minimum value of \( \alpha + \beta \).

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