
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 $120$ meters. Cara leaves $C$ and skates at a speed of $8$ meters per second on a straight line that makes a $45^\circ$ angle with $CD$. Simultaneously, Danny leaves $D$ at a speed of $7$ meters per second and follows the straight path that leads to the earliest possible meeting with Cara, given their speeds. How far does Cara skate before meeting Danny?

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