
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 $ABCD-A_{1}B_{1}C_{1}D_{1}$ with edge length 1, $E$ is the midpoint of $AB$, and $F$ is the midpoint of $CC_{1}$. Find the distance from $D$ to the plane passing through points $D_{1}$, $E$, and $F$.


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