
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, Amy and Bob, are at points $A$ and $B$, respectively, on a flat frozen lake. The distance between $A$ and $B$ is $120$ meters. Amy leaves $A$ and skates at a speed of $9$ meters per second on a straight line that makes a $45^\circ$ angle with $AB$. At the same time Amy leaves $A$, Bob leaves $B$ at a speed of $10$ meters per second and skates directly towards $A$. How many meters does Amy skate before meeting Bob?

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