
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 model car is tested on some closed circuit  $600$  meters long, consisting of flat stretches, uphill and downhill. All uphill and downhill have the same slope. The test highlights the following facts:

[list]
(a) The velocity of the car depends only on the fact that the car is driving along a stretch of uphill, plane or downhill; calling these three velocities  $v_s, v_p$  and  $v_d$  respectively, we have  $v_s <v_p <v_d$ ;

(b)  $v_s,v_p$  and  $v_d$ , expressed in meter per second, are integers.

(c) Whatever may be the structure of the circuit, the time taken to complete the circuit is always  $50$  seconds.
[/list]

Find all possible values of  $v_s, v_p$  and  $v_d$ .

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