
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 sides of the equilateral triangle $ABC$ are $6 \mathrm{~cm}$ long. A bug moves uniformly from vertex $C$ towards vertex $A$ at a speed of $4 \mathrm{~mm} / \mathrm{s}$. At the same time, another bug moves from vertex $B$ towards vertex $C$ at a speed of $3 \mathrm{~mm} / \mathrm{s}$. How much time will pass from the start until they are closest to each other, and what is this shortest distance?

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