
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
Natural numbers $1, 2, 3, 4, \cdots$ are arranged in order according to the direction indicated by arrows, and they turn at positions of numbers like $2, 3, 5, 7, 10, \cdots$ and so on.
(1) If 2 is counted as the first turn, then the number at the 45th turn is $\qquad$ .
(2) From 1978 to 2010, the natural numbers that are exactly at turning positions are $\qquad$ .

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