
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 stones are thrown simultaneously with the same initial speed $v_{0}$. The first stone is thrown horizontally from a height $H=50$ meters, and the second stone is thrown vertically upwards from the surface of the Earth. It is known that the stones collided in the air. Determine the initial distance between the stones. Neglect air resistance.

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