
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
Along the sides of a right angle, two spheres with radii of 2 cm and 3 cm move towards the vertex. The centers of these spheres move along the sides of the angle with unequal but constant speeds. At a certain moment, the center of the smaller sphere is 6 cm from the vertex, and the center of the larger sphere is 16 cm from the vertex. After 1 second, the distance between the centers becomes 13 cm, and 2 seconds later, the spheres collide before reaching the vertex. Find the speeds of the spheres.

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