
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
Kristýna chose a certain odd natural number divisible by three. Jakub and David then examined triangles with a perimeter in millimeters equal to the number chosen by Kristýna, where the sides have lengths in millimeters expressed as mutually distinct integers.

Jakub found a triangle in which the longest side has the maximum possible length and wrote this value on the board. David found a triangle in which the shortest side has the maximum possible length and wrote this value on the board as well. Kristýna correctly added both lengths on the board and got $1681 \mathrm{~mm}$.

Determine the number Kristýna chose.

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