
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
Two ants, Gosha and Lesha, are crawling along the diagonals of the bases $AC$ and $B_{1}D_{1}$ of a cube $ABCDA_{1}B_{1}C_{1}D_{1}$ with edge length $a$. They started crawling simultaneously from points $A$ and $B_{1}$ respectively with constant speeds, where Lesha's speed was five times that of Gosha's speed. Lesha finishes crawling when he reaches point $D_{1}$. What is the minimum distance that separated Gosha and Lesha during their movement?

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