
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 vertices of a cube ABCD-A1B1C1D1 with edge length $a$ are all on the surface of a sphere $O$. $E$ and $F$ are the midpoints of edges $AA1$ and $DD1$, respectively. The length of the line segment cut off by sphere $O$ from line $EF$ is __________.

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