
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
At the intersection of roads $A$ and $B$ (lines) there is a settlement $C$ (point). Sasha is walking along road $A$ towards point $C$, taking 50 steps per minute, with a step length of 50 cm. At the beginning of the movement, Sasha was at a distance of 250 meters from point $C$. Dania is walking towards $C$ along road $B$ at a speed of 80 steps per minute, with a step length of 40 cm, and at the start of their joint movement, Dania was at a distance of 300 meters from $C$. After passing point $C$, each of them, without stopping, continues to move along their road. We record the moments in time when Dania and Sasha each take an integer number of steps. Find the minimum possible distance between them (along the roads) at such moments in time. How many steps has each of them taken by the time this distance is minimized?

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