
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 skaters, Cara and Danny, are at points \(C\) and \(D\) respectively, on a flat, frozen lake. The distance between \(C\) and \(D\) is 100 meters. Cara leaves \(C\) and skates at a speed of \(9\) meters per second on a straight line that makes a \(75^\circ\) angle with \(CD\). Simultaneously, Danny leaves \(D\) at a speed of \(6\) meters per second and follows the straight path that allows for the earliest possible meeting with Cara, given their speeds. Calculate how many meters Cara skates before meeting Danny.

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