
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
Given six thin sticks with lengths of 3, 8, 12, 15, 17, and 18 cm, respectively, if three of them are selected and connected end to end in sequence to form a right-angled triangle, determine the lengths of these three thin sticks.

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