
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

The Gregorian calendar defines a common year as having 365 days and a leap year as having 366 days. The $n$-th year is a leap year if and only if:

1. $n$ is not divisible by 100 and $n$ is divisible by 4, or
2. $n$ is divisible by 100 and $n$ is divisible by 400.

For example, 1996 and 2000 are leap years, whereas 1997 and 1900 are not. These rules were established by Pope Gregory XIII.

Given that the "Gregorian year" is fully aligned with the astronomical year, determine the length of an astronomical year.

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