
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 hikers, Alice and Bob, start at points $P$ and $Q$, respectively, on a straight forest path. The distance between $P$ and $Q$ is $150$ meters. Alice leaves $P$ and walks at a speed of $6$ meters per second on a straight line that makes a $45^\circ$ angle with $PQ$. At the same time Alice leaves $P$, Bob leaves $Q$ at a speed of $5$ meters per second and follows the straight path that produces the earliest possible meeting of the two hikers. How many meters does Alice walk before meeting Bob?

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