
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
A sequence of numbers: 0, 1, 2, 3, 6, 7, 14, 15, 30, ( ), ( ), ( ); this sequence was written down by Xiao Ming following a certain rule. He first wrote down "0, 1", then continued with "2, 3", followed by "6, 7", and then "14, 15", continuing in this manner. What should be the last three numbers of this sequence?

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