
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 number is called lucky if computing the sum of the squares of its digits and repeating this operation sufficiently many times leads to number  $1$ . For example,  $1900$  is lucky, as  $1900 \to 82 \to 68 \to 100 \to 1$ . Find infinitely many pairs of consecutive numbers each of which is lucky.

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