
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
A right triangle with legs of length \( l = 1 \) meter is made from wire. Two bugs start crawling simultaneously from vertices A and B along the legs, with speeds \( v_A = 5 \) cm/s and \( v_B = 2v_A = 10 \) cm/s. What is the minimum time after the start of their movement for the distance between the bugs to reach its minimum?

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