
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 steamboats are expected to arrive in Odessa with a one-hour interval. Both steamboats travel at the same speed, but circumstances unfolded such that the first steamboat would be late by $t_{1}$ minutes, and the second by $t_{2}$ minutes. Upon receiving radio instructions to arrive on time, both captains simultaneously increased their steamboats' speeds: the first by $v_{1}$ km/h, the second by $v_{2}$ km/h, resulting in both steamboats arriving in Odessa exactly on schedule. What was the speed of the steamboats before receiving the radio signal?

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