
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 the cube \(ABCD-A_{1}B_{1}C_{1}D_{1}\), \(E\) is the midpoint of \(BC\), and \(F\) is on \(AA_{1}\) such that the ratio \(A_{1}F : FA = 1 : 2\). Find the dihedral angle between plane \(B_{1}EF\) and the base \(A_{1}B_{1}C_{1}D_{1}\).

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