
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 cyclists, Alex and Blake, start from points $X$ and $Y$ respectively, 150 meters apart on a straight road. Alex cycles away from $Y$ at a speed of 10 meters per second along a straight line making a $45^\circ$ angle with $XY$. Simultaneously, Blake cycles at a speed of 9 meters per second and follows the straight path that results in the earliest possible meeting with Alex. Determine how many meters Alex cycles before meeting Blake.

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