
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 skiers, Dan and Eva, start from points $D$ and $E$ respectively on a snow-covered field. The distance between $D$ and $E$ is $200$ meters. Dan leaves $D$ and skis at a speed of $10$ meters per second on a straight line that makes a $45^\circ$ angle with $DE$. Simultaneously, Eva leaves $E$ at a speed of $15$ meters per second and follows the straight path that allows her to meet Dan as soon as possible, given their speeds. Calculate how many meters Dan skis before meeting Eva.

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