
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 joggers, Claire and Dylan, meet at opposite sides of a park. Claire starts at point $C$ and Dylan at point $D$. The distance between $C$ and $D$ is 200 meters. Claire jogs at a speed of 5 meters per second along a straight path that makes a $45^\circ$ angle with $CD$. Simultaneously, Dylan jogs from $D$ at a speed of 6 meters per second and takes a direct route that brings about the earliest meeting. Determine how far Claire has jogged when they first meet.

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