
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
On a plate, there are different candies of three types: 2 lollipops, 3 chocolate candies, and 5 jelly candies. Sveta ate all of them one by one, choosing each next candy at random. Find the probability that the first and last candies she ate were of the same type.

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