
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
On a frozen lake, Mia starts at point $X$ and Noah starts at point $Y$. The distance between $X$ and $Y$ is 150 meters. When they start moving, Mia skates at a speed of 10 meters per second following a straight path that forms a $45^\circ$ angle with $XY$. At the same time, Noah skates from $Y$ towards Mia at a speed of 9 meters per second, aiming to intercept her path as quickly as possible. Calculate the distance Mia skates before meeting Noah.

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