
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
A straight line connects City A at  $(0, 0)$  to City B, 300 meters away at  $(300, 0)$ . At time  $t=0$ , a bullet train instantaneously sets out from City A to City B while another bullet train simultaneously leaves from City B to City A going on the same train track. Both trains are traveling at a constant speed of  $50$  meters/second. 

Also, at  $t=0$ , a super 
y stationed at  $(150, 0)$  and restricted to move only on the train tracks travels towards City B. The 
y always travels at 60 meters/second, and any time it hits a train, it instantaneously reverses its direction and travels at the same speed. At the moment the
trains collide, what is the total distance that the y will have traveled? Assume each train is a point
and that the trains travel at their same respective velocities before and after collisions with the y

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