
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 $ABCDA_1B_1C_1D_1$, $E$ is the midpoint of $BC$, and $F$ is on $AA_1$ such that $A_1F : FA = 1 : 2$. Find the dihedral angle between plane $B_1EF$ and the base $A_1B_1C_1D_1$.

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