
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 \( B \) (straight lines) there is a settlement \( C \) (a point). Sasha walks along road \( A \) towards point \( C \), taking 40 steps per minute, with a step length of 65 cm. At the beginning of the walk, Sasha was at a distance of 260 m from point \( C \). Dania walks towards \( C \) along road \( B \) at a speed of 75 steps per minute, with a step length of 50 cm and at the beginning of their joint movement was at a distance of 350 m from \( C \). Each of them, having passed point \( C \), continues to walk along their road without stopping. Consider moments when Dania and Sasha have each taken an integer number of steps. Find the minimum possible distance between them (along the roads) at such moments of 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}
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