
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 distant planet in the mangrove forests, there is a population of frogs. The number of frogs born each year is 1 more than the difference between the number of frogs born in the previous two years (subtracting the smaller number from the larger one).

For example, if 5 frogs were born last year and 2 the year before that, then 4 frogs will be born this year; if 3 frogs were born last year and 10 the year before that, then 8 frogs will be born this year.

In the year 2020, 2 frogs were born, and in 2021, 9 frogs were born. In the closest year, when will exactly 1 frog be born for the first time?

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