
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
Inside a cube with edge length $a$, there is an inscribed sphere. A line passes through the midpoints of two edges of the cube that are a pair of opposite edges of a face. Find the length of the segment of this line that is inside the sphere.

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