
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
Point  $P_1$  is located  $600$  miles West of point  $P_2$ . At  $7:00\text{AM}$  a car departs from  $P_1$  and drives East at a speed of  $50$ mph. At  $8:00\text{AM}$  another car departs from  $P_2$  and drives West at a constant speed of  $x$  miles per hour. If the cars meet each other exactly halfway between  $P_1$  and  $P_2$ , what is the value of  $x$ ?

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